Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Peter]

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>At present, all notable proof-of-work currencies reward miners with both a block reward, and transaction fees. With most currencies (including Bitcoin) phasing out block rewards over time. However in no currency have transaction fees consistently been more than 5% to 10% of the total mining reward[^fee-in-reward], with the exception of Ethereum, from June 2020 to Aug 2021. To date no proof-of-work currency has ever operated solely on transaction fees[^pow-tweet], and academic analysis has found that in this condition block generation is unstable.[^instability-without-block-reward] To paraphrase Andrew Poelstra, it's a scary phase change that no other coin has gone through.[^apoelstra-quote]

We should consider that a fixed block reward doesn't guarantee that the value of energy securing transactions is greater than the value being transacted in a practical amount of blocks where practical is a certain amount of time (currently 1 hour). If the energy expenditure is less than the value transacted in a given amount of blocks those transactions are at risk of being double spent. We have seen this failure with Ethereum Classic where any meaningful amount of value would need 2 weeks of blocks to be deeply confirmed for economic purposes.

We should also not assume that the Bitcoin emission curve implies there will be zero block rewards for mining Bitcoin, let me explain. There's an ugly solution that doesn't require a hard fork (I'm not advocating for this solution just presenting it) where a new coin is launched to merge mine with Bitcoin and that new coin (called BTail for discussion purposes) would enfranchise everyone who is a Bitcoin UTXO holder at the moment of the real-time launch of BTail at a well known block height. Using a technique we have seen with BCH to create an arguably fair launch. BTail would have a floating exchange rate to Bitcoin and its success or failure in terms of adoption would be determined by the market. It would require the same network effect barriers as a hard fork (opt-in) but would not put Bitcoin at risk while people can take time to install new software (and write new integrations) as they would with a soft fork.

Regards

Peter Kroll

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Billy Tetrud]

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@vjudeu
> Miners can game this system by moving their own coins in 100% fees
transactions, just to produce more coins. You have one million BTC? No
problem, just move them as fees, and you just created 100k BTC out of thin
air, just because you are a wealthy miner.

Hmm, I believe you're right about that. If a miner can make 1 BTC of fees
by honestly mining + 0.1 BTC of inflation, they could instead make 2 BTC by
mining their own transactions with 20 BTC of fees. That does sound very
gameable. I rescind my suggestion.

One could imagine modifications to that suggestion that attempts to make it
more difficult to game directly. For example, if an average sum of
fees/block was calculated over a window (eg 2 weeks, 2 months, etc) and 10%
of that was released in coinbase rewards, you would eliminate the
possibility for individual miners to game the system. However, you would
then have to consider the group of miners as a whole - since they all have
an interest in increasing their revenues, it certainly seems like a
dangerous incentive that could lead to runaway inflation. So perhaps even
extensions of my suggestion are too gameable to be safe.

But my point still stands that tail emission is not a permanent solution.
One permanent solution would be some constant inflation *rate *(eg
0.1%/year). Given that the necessary security is a function of the total
value of the currency, perhaps that would be a reasonable natural way to
scale security as needed.

Again tho, I haven't seen any convincing evidence that any solution like
this will likely be necessary at all. Total collected fees will also scale
up as bitcoin grows, probably quadratically (since the value of the network
grows quadratically). I'm rather more inclined to think collected fees will
get far *too* high - ie substantially higher than needed to pay for
sufficient blockchain security.




On Fri, Aug 19, 2022 at 1:48 PM aliashraf.btc At protonmail via bitcoin-dev
<bitcoin-dev@lists.linuxfoundation.org> wrote:

> Hi Peter, everyone
> This issue has been discussed thoroughly in bitcointalk, general
> discussions are more suited to forums, I believe, still ....
>
> First and foremost, it is more than obvious that bitcoin block subsidy
> algorithm is a total disaster, not just for the zero subsidy security
> consequences, but also for the overly rewarding scheme that favors (few)
> first-runners against (masses of) people who join later, a policy that
> looks to be a cheap marketing trick rather than a decent strategic
> monetary, system design, no matter how natural it is presumed nowadays,
> after being implemented by Bitcoin.
>
> For now, the brilliance of the idea behind Bitcoin and the enthusiasm have
> compensated for its bizzar, upside-down inflation policy, in practice as
> newcomers have been paying the price to lucky first-runners and adopting
> anyway.
> Is it happening for low block subsidy? Is it going to be solved somehow? I
> don't think so.
>
> With subsidy still being the major (like 90%) portion of the block reward,
> there is an equalizer factor pushing equilibrium by paying security costs
> on behalf of current coin owners.Note that every single new bitcoin paid as
> subsidy is actually paid by the rest of the wallets proportional to their
> balance.
> Other than its direct contribution to security, once understood as a
> ballance-based taxing scheme, it is a crucial mechanism for re-distribution
> of wealth because to compensate for their costs, unlike speculators (who
> are among the worst adopters of Bitcoin, and unfortunately the most
> influencers), miners are used to dumping their coins, providing more fair
> opportunities for people to join.
> So, halving and the hard cap, put both adoption and security as risk, It
> is why, unlike  "believers", I'm deeply concerned about a future with low
> block subsidy because it puts both security and adoption in an awkward
> situation.
>
> Additionally, It is not considered an engineering practice by any measure
> to speculate about the security of a system that we abundantly recommend to
> friends, family for joining.
> We need proofs, security proof, ease of adaptation proof, etc.,
> Fantasies are not proofs, having faith in a magical incentive mechanism
> that fixes everything is not an argument, let alone being a proof.
> Incentives are irrelevant, rules, schemes, projects, and so fort, matter.
> There are always incentives in games, but rules are in charge of
> determining the fate.
> Without rules, there is no game, flawed schemes and rules move the game
> behind its equilibrium to fail eventually.
>
> I've not to mention the unfeasibility of tempering Bitcoin's basic
> consensus rules, Bitcoin rules are not subject to change specially when it
> comes to something that is widely considered a basic characteristic, a
> Schelling point, and so forth.
>
> So, it is the paradoxical situation: we are exposed to, on one hand, it is
> a deficiency and on the other hand it is inevitable because is critically
> hard-code to Bitcoin, advertised more than any feature as its identity.
> But it is our job, isn't it? Dealing with the impossible and taking care
> of it, but I think before reaching to that point we have to settle the
> basics.:
>
>
>    1. There is a problem with long term security and adoption
>    consequences.
>    2. It is built deeply to bitcoin consensus rules, and considered a
>    critical
>    3. It is not going to disappear magically, neither it will be
>    addressed by whales, etc.
>    4. The 21M cap, halving, and generally, Bitcoin consensus, is not
>    subject to change.
>
>
> Don't panic, it is not exactly a catch-22 situation. Tip:
> It is always possible to help a system without aggressive intervention,
> either by smart tweaks or by supporting it using other system(s).
>
> Cheers, Ali Ashraf
>
>
>
> ------- Original Message -------
> On Tuesday, August 16th, 2022 at 8:35 PM, Peter via bitcoin-dev <
> bitcoin-dev@lists.linuxfoundation.org> wrote:
>
> Hi Jaroslaw,
>
>
>
> In the Prisoner's Dilemma the prisoners cannot communicate. In Bitcoin
> large holders are able to communicate with each other. Also, prisoners need
> not make an all or nothing decision in Bitcoin. Miners can join and leave
> the network freely over time. You can change your decision based on the
> decision of others.
>
>
> The Bitcoin design is such that security is volatile but the issuance of
> blocks is timely and evened out to a 10 minutes average even after the
> reward is exhausted.
>
>
> The existing incentive that miners earn money for including transactions
> is enough to motivate human nature. Transaction initiators have an
> incentive to mine and run full nodes for personal interest.
>
>
> >Noone will waste his renewable energy on unprofitable Antminer while
> he/she can sell this energy for the market price.
>
>
> The law in most jurisdictions prevents the resale of spare electricity
> unless an expensive license is obtained (and in most cases no license is
> available as the government maintains a monopoly). Mining with waste
> electricity is reducing losses. Another incentive to motivate human nature.
>
>
> Bitcoin holders can be enfranchised into any new system. So, no need for
> bike shedding the original design which is a Schelling Point.
>
>
> Regards
>
> Peter Kroll
>
> pointbiz/ BTCCuracao
>
>
>
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[aliashraf.btc At protonmail]

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Hi Peter, everyone
This issue has been discussed thoroughly in bitcointalk, general discussions are more suited to forums, I believe, still ....

First and foremost, it is more than obvious that bitcoin block subsidy algorithm is a total disaster, not just for the zero subsidy security consequences, but also for the overly rewarding scheme that favors (few) first-runners against (masses of) people who join later, a policy that looks to be a cheap marketing trick rather than a decent strategic monetary, system design, no matter how natural it is presumed nowadays, after being implemented by Bitcoin.

For now, the brilliance of the idea behind Bitcoin and the enthusiasm have compensated for its bizzar, upside-down inflation policy, in practice as newcomers have been paying the price to lucky first-runners and adopting anyway.
Is it happening for low block subsidy? Is it going to be solved somehow? I don't think so.

With subsidy still being the major (like 90%) portion of the block reward, there is an equalizer factor pushing equilibrium by paying security costs on behalf of current coin owners.Note that every single new bitcoin paid as subsidy is actually paid by the rest of the wallets proportional to their balance.
Other than its direct contribution to security, once understood as a ballance-based taxing scheme, it is a crucial mechanism for re-distribution of wealth because to compensate for their costs, unlike speculators (who are among the worst adopters of Bitcoin, and unfortunately the most influencers), miners are used to dumping their coins, providing more fair opportunities for people to join.
So, halving and the hard cap, put both adoption and security as risk, It is why, unlike "believers", I'm deeply concerned about a future with low block subsidy because it puts both security and adoption in an awkward situation.

Additionally, It is not considered an engineering practice by any measure to speculate about the security of a system that we abundantly recommend to friends, family for joining.
We need proofs, security proof, ease of adaptation proof, etc.,
Fantasies are not proofs, having faith in a magical incentive mechanism that fixes everything is not an argument, let alone being a proof.
Incentives are irrelevant, rules, schemes, projects, and so fort, matter. There are always incentives in games, but rules are in charge of determining the fate.
Without rules, there is no game, flawed schemes and rules move the game behind its equilibrium to fail eventually.

I've not to mention the unfeasibility of tempering Bitcoin's basic consensus rules, Bitcoin rules are not subject to change specially when it comes to something that is widely considered a basic characteristic, a Schelling point, and so forth.

So, it is the paradoxical situation: we are exposed to, on one hand, it is a deficiency and on the other hand it is inevitable because is critically hard-code to Bitcoin, advertised more than any feature as its identity.
But it is our job, isn't it? Dealing with the impossible and taking care of it, but I think before reaching to that point we have to settle the basics.:

- There is a problem with long term security and adoption consequences.
- It is built deeply to bitcoin consensus rules, and considered a critical
- It is not going to disappear magically, neither it will be addressed by whales, etc.
- The 21M cap, halving, and generally, Bitcoin consensus, is not subject to change.

Don't panic, it is not exactly a catch-22 situation. Tip:
It is always possible to help a system without aggressive intervention, either by smart tweaks or by supporting it using other system(s).

Cheers, Ali Ashraf

------- Original Message -------
On Tuesday, August 16th, 2022 at 8:35 PM, Peter via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org> wrote:

> Hi Jaroslaw,

> In the Prisoner's Dilemma the prisoners cannot communicate. In Bitcoin large holders are able to communicate with each other. Also, prisoners need not make an all or nothing decision in Bitcoin. Miners can join and leave the network freely over time. You can change your decision based on the decision of others.
>
> The Bitcoin design is such that security is volatile but the issuance of blocks is timely and evened out to a 10 minutes average even after the reward is exhausted.
>
> The existing incentive that miners earn money for including transactions is enough to motivate human nature. Transaction initiators have an incentive to mine and run full nodes for personal interest.
>
>>Noone will waste his renewable energy on unprofitable Antminer while he/she can sell this energy for the market price.
>
> The law in most jurisdictions prevents the resale of spare electricity unless an expensive license is obtained (and in most cases no license is available as the government maintains a monopoly). Mining with waste electricity is reducing losses. Another incentive to motivate human nature.
>
> Bitcoin holders can be enfranchised into any new system. So, no need for bike shedding the original design which is a Schelling Point.
>
> Regards
>
> Peter Kroll
>
> pointbiz/ BTCCuracao

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[vjudeu]

> If we actually wanted to solve the potential problem of not-enough-fees to upkeep mining security, there are less temporary ways to solve that. For example, if fees end up not being able to support sufficient mining, we could add emission based on a constant fraction of fees in the block. For example, every block could emit new bitcoin amounting to 10% of the fees collected in that block. This would tie coinbase rewards to the real world (since the fee market is tied to the real economy) and ensure higher block revenue indefinitely - ie not just for another 50 years.

Miners can game this system by moving their own coins in 100% fees transactions, just to produce more coins. You have one million BTC? No problem, just move them as fees, and you just created 100k BTC out of thin air, just because you are a wealthy miner. And even if that amount will be stolen, when some other miner will reorg your block, then still, miners will keep creating coins by moving them as fees, and the strongest miner will get the whole pot. And guess what: 100 blocks later you can reuse newly created 100k BTC to make another 10k BTC, so it will exponentially explode as (amountOfCoins*(1+0.1))^n function. And guess what: (1.1)^8 is 2.14358881. That means, after eight moves, you can double your coins, if you are a wealthy miner. And you can start with smaller amounts, to play it safe, but eventually, this system will degrade into "coin doubler after 800 blocks" or something similar.


On 2022-08-18 18:45:43 user Billy Tetrud via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org> wrote:
While constant tail emission does in fact converge to 0 inflation over time (which bitcoin's halvings do as well mind you), tail emission does *not* solve the potential problem of mining rewards, it only delays it. A tail emission of 200,000 btc/year (~1% of the current supply) would be equivalent to halvings every ~50 years rather than every 4 years. Were we to implement this kind of thing right after the last non-" destructive" halving, it would buy us 46 years of extra time. Nothing more, nothing less.


While its mildly interesting to know that tail emission converges to a stable point, while no inflation implies monetary deflation at the rate of loss, this feels very likely to be an insignificant problem. I think 1% loss rate per year is an absurdly high estimate these days, and the loss rate is likely to decrease as methods of storing bitcoin mature. Imagine bitcoin was worth $1 trillion (not so hard, since it was not too long ago), then try imagining people losing $10 billion of bitcoin every year. Highly unlikely IMO. A rate of loss of 0.01%/year might be more realistic for a near-future mature bitcoin. That's not going to be enough to make a significant difference even over 100s of years. 


If we actually wanted to solve the potential problem of not-enough-fees to upkeep mining security, there are less temporary ways to solve that. For example, if fees end up not being able to support sufficient mining, we could add emission based on a constant fraction of fees in the block. For example, every block could emit new bitcoin amounting to 10% of the fees collected in that block. This would tie coinbase rewards to the real world (since the fee market is tied to the real economy) and ensure higher block revenue indefinitely - ie not just for another 50 years. 


But its also worth saying that blockchain security (which mining revenue correlates with) does *not* need to increase indefinitely. There is some amount of security (and therefore some amount of mining revenue) that is sufficient, beyond which additional security is simply unnecessary, unwarranted, and wasteful (you wouldn't buy a $1000 safe to store $1000 of valuables). Do we, as the bitcoin community, have some good idea how much security we need? Do we have some idea how costly a 51% attack must be where we can be comfortable it will never happen? I'm curious to hear what people think about that. Because without having some kind of estimates of what "enough security" is, there's absolutely no way of evaluating whether or not its likely that bitcoin fees alone will be able to sustain enough security. 






On Wed, Aug 17, 2022 at 9:31 AM Jaroslaw via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org> wrote:

On one scale you puts the Trust to the large stakeholders (why we avoid plenty of small stakeholders, btw),
and on the other side I put game theory and well defined Prisoner's Dilemma.

Again: large stakeholders WILL NOT incentivised to mine, they will have the hundreds excuses why not to switch-on Antminers back.
That's how it simply works.  Bitcoin would fail miserably if Satoshi was based his concept mainly on existence of idealists.

If we will observe lack of hashrate recovery four years after some halving and still unprepared like today
- means the trust in large stakeholders was a very costly mistake.


Superiority of Proof of Work against Proof of Stake has been discussed enough either
The overall conclusion with what I fully agree  is: swapping PoW to PoS - would be a degradation.
You can stop talking about degradation to proof of stake, but just: degradation.

Degradation of Bitcoin, due to human greed.

Now you mine and you have an INSTANT gratification.
Then you will mine and it will cost you real money, but simple switch - and you have a DELAYED, maybe some day in the future, maybe only a tiny - punishment.
And The Punishment Won't Be Tiny.


"If the pain after hitting the hand with a hammer would appear after a month - people would notoriously walk with swollen fingers"
100% (^2)

Regards
Jaroslaw



W dniu 2022-08-17 13:10:38 użytkownik Erik Aronesty <erik@q32.com> napisał:

> you can stop talking about  the "security of the system" as meaningful
> this has been discussed enough
> if fees are not sufficient, clearance times increase and large stakeholders are incentivised to mine 
> in the best case, fees are sufficient
> in the worst case, it degrades to proof of stake
> i'm sure you can see how that's fine either way



_______________________________________________
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https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev


_______________________________________________
bitcoin-dev mailing list
bitcoin-dev@lists.linuxfoundation.org
https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev

_______________________________________________
bitcoin-dev mailing list
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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Erik Aronesty]

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1...
>  Degradation

Remember, if hash rate declines (no sign that it will so far), the
net-effect is longer clearance times for large transactions.

It's not "failure" or "breaking"

2...
Certainly, if demand for blockspace isn't high enough to support clearance
then the *first *thing to do would be to improve the utility of the chain
so that demand for blockspace is high.

This is one of the strong reasons to support research like covenants and
rgb and taro.   If those tools become popular, we will see rising fees.
 Indeed, large miners should be *paying* researchers to advance these
tools.   It's in their own best interests.

3...
> and on the other side I put game theory and well defined Prisoner's
Dilemma.

The prisoner's dilemma does not state that zero stakeholders will
mine, just far fewer.   Real world experiments with actual prisoners and
students show cooperation rates of 33%.  Plus there are incentives.
Stakeholders who want to move large amounts in a reasonable amount of time
are incentivised to mine.

4...
Changing issuance is a non-starter, forte very game-theoretic reasons you
refer to

it would destroy the value proposition of the chain, fork the coin and i
have every confidence that the surviving fork would be the one without the
new issuance


On Wed, Aug 17, 2022 at 9:43 AM <jk_14@op.pl> wrote:

>
> On one scale you puts the Trust to the large stakeholders (why we avoid
> plenty of small stakeholders, btw),
> and on the other side I put game theory and well defined Prisoner's
> Dilemma.
>
> Again: large stakeholders WILL NOT incentivised to mine, they will have
> the hundreds excuses why not to switch-on Antminers back.
> That's how it simply works.  Bitcoin would fail miserably if Satoshi was
> based his concept mainly on existence of idealists.
>
> If we will observe lack of hashrate recovery four years after some halving
> and still unprepared like today
> - means the trust in large stakeholders was a very costly mistake.
>
>
> Superiority of Proof of Work against Proof of Stake has been discussed
> enough either
> The overall conclusion with what I fully agree  is: swapping PoW to PoS -
> would be a degradation.
> You can stop talking about degradation to proof of stake, but just:
> degradation.
>
> Degradation of Bitcoin, due to human greed.
>
> Now you mine and you have an INSTANT gratification.
> Then you will mine and it will cost you real money, but simple switch -
> and you have a DELAYED, maybe some day in the future, maybe only a tiny -
> punishment.
> And The Punishment Won't Be Tiny.
>
>
> "If the pain after hitting the hand with a hammer would appear after a
> month - people would notoriously walk with swollen fingers"
> 100% (^2)
>
> Regards
> Jaroslaw
>
>
>
> W dniu 2022-08-17 13:10:38 użytkownik Erik Aronesty <erik@q32.com>
> napisał:
>
> > you can stop talking about  the "security of the system" as meaningful
> > this has been discussed enough
> > if fees are not sufficient, clearance times increase and large
> stakeholders are incentivised to mine
> > in the best case, fees are sufficient
> > in the worst case, it degrades to proof of stake
> > i'm sure you can see how that's fine either way
>
>
>
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>
>
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>
>

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[jk_14]

Fortunately halving in 2020 will be non destructive because it looks like we will have higher difficulty in 2024 than in 2020.

Let's assume the worst case scenario: after halving in 2024, we have regression of difficulty in 2028. Annual inflation rate in 2028 is 0.81%. Removal of halvings in this year means that in year 2100 (72 years later) we will have 0.51% annual inflation rate, still. And that is Monero concept in fact: constant annual supply, thus very slowly decreasing of inflation.

Yes, you are right. Better that that - would be to wait for bitcoin ecosystem to show us what is the equilibrium/saturation level at globe scale - I hope it will be several years later and "the annual inflation to keep" - will be 0.40% in 2032 or even 0.20% only in 2036.

And then instead of halving every 210k blocks - just to adjust the block reward (i.e. slightly increase). To keep the annual inflation rate constant. Constant forever. On most proper level - because determined empirically. I didn't propose it, because of certain, immediate backlash :)

And for the same reason, as an answer how much security we need. Empirically reached security level is - the most accurate one. In military terminology: the protection of already conquered land. Regression is sign of weakness and we probably don't want to see it in Bitcoin.

Anyway, keeping Bitcoin in the middle of ultra-obvious Edge Case, with pathological Friedman's "free lunches" for stakeholders, due to this overtaxing (punish) people which are simply want to use Bitcoin, additionally with pure form of Prisoner's Dilemma here, and with Trust to "large" stakeholders, while almost every of them will convince himself he is not really a large one and "let Microstrategy run Antminers" (and burn money)

- and all above only because we are too greed to pay miners as low as only few tenths of a percent per year for their real service as keeping network secure, pay in most honest way, because with no exceptions and proportionally to holdings - and instead of it we rather prefer to take the high risk of spiral of death - is madness.


Pure madness. This is what almost 50y old cynic may assure you.

Regards
Jaroslaw




W dniu 2022-08-18 17:44:29 użytkownik Billy Tetrud <billy.tetrud@gmail.com> napisał:
While constant tail emission does in fact converge to 0 inflation over time (which bitcoin's halvings do as well mind you), tail emission does *not* solve the potential problem of mining rewards, it only delays it. A tail emission of 200,000 btc/year (~1% of the current supply) would be equivalent to halvings every ~50 years rather than every 4 years. Were we to implement this kind of thing right after the last non-" destructive" halving, it would buy us 46 years of extra time. Nothing more, nothing less.

While its mildly interesting to know that tail emission converges to a stable point, while no inflation implies monetary deflation at the rate of loss, this feels very likely to be an insignificant problem. I think 1% loss rate per year is an absurdly high estimate these days, and the loss rate is likely to decrease as methods of storing bitcoin mature. Imagine bitcoin was worth $1 trillion (not so hard, since it was not too long ago), then try imagining people losing $10 billion of bitcoin every year. Highly unlikely IMO. A rate of loss of 0.01%/year might be more realistic for a near-future mature bitcoin. That's not going to be enough to make a significant difference even over 100s of years. 

If we actually wanted to solve the potential problem of not-enough-fees to upkeep mining security, there are less temporary ways to solve that. For example, if fees end up not being able to support sufficient mining, we could add emission based on a constant fraction of fees in the block. For example, every block could emit new bitcoin amounting to 10% of the fees collected in that block. This would tie coinbase rewards to the real world (since the fee market is tied to the real economy) and ensure higher block revenue indefinitely - ie not just for another 50 years. 

But its also worth saying that blockchain security (which mining revenue correlates with) does *not* need to increase indefinitely. There is some amount of security (and therefore some amount of mining revenue) that is sufficient, beyond which additional security is simply unnecessary, unwarranted, and wasteful (you wouldn't buy a $1000 safe to store $1000 of valuables). Do we, as the bitcoin community, have some good idea how much security we need? Do we have some idea how costly a 51% attack must be where we can be comfortable it will never happen? I'm curious to hear what people think about that. Because without having some kind of estimates of what "enough security" is, there's absolutely no way of evaluating whether or not its likely that bitcoin fees alone will be able to sustain enough security. 


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bitcoin-dev mailing list
bitcoin-dev@lists.linuxfoundation.org
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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Billy Tetrud]

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While constant tail emission does in fact converge to 0 inflation over time
(which bitcoin's halvings do as well mind you), tail emission does *not*
solve the potential problem of mining rewards, it only delays it. A tail
emission of 200,000 btc/year (~1% of the current supply) would be
equivalent to halvings every ~50 years rather than every 4 years. Were we
to implement this kind of thing right after the last non-" destructive"
halving, it would buy us 46 years of extra time. Nothing more, nothing less.

While its mildly interesting to know that tail emission converges to a
stable point, while no inflation implies monetary deflation at the rate of
loss, this feels very likely to be an insignificant problem. I think 1%
loss rate per year is an absurdly high estimate these days, and the loss
rate is likely to decrease as methods of storing bitcoin mature. Imagine
bitcoin was worth $1 trillion (not so hard, since it was not too long ago),
then try imagining people losing $10 billion of bitcoin every year. Highly
unlikely IMO. A rate of loss of 0.01%/year might be more realistic for a
near-future mature bitcoin. That's not going to be enough to make a
significant difference even over 100s of years.

If we actually wanted to solve the potential problem of not-enough-fees to
upkeep mining security, there are less temporary ways to solve that. For
example, if fees end up not being able to support sufficient mining, we
could add emission based on a constant fraction of fees in the block. For
example, every block could emit new bitcoin amounting to 10% of the fees
collected in that block. This would tie coinbase rewards to the real world
(since the fee market is tied to the real economy) and ensure higher block
revenue indefinitely - ie not just for another 50 years.

But its also worth saying that blockchain security (which mining revenue
correlates with) does *not* need to increase indefinitely. There is some
amount of security (and therefore some amount of mining revenue) that is
sufficient, beyond which additional security is simply unnecessary,
unwarranted, and wasteful (you wouldn't buy a $1000 safe to store $1000 of
valuables). Do we, as the bitcoin community, have some good idea how much
security we need? Do we have some idea how costly a 51% attack must be
where we can be comfortable it will never happen? I'm curious to hear what
people think about that. Because without having some kind of estimates of
what "enough security" is, there's absolutely no way of evaluating whether
or not its likely that bitcoin fees alone will be able to sustain enough
security.



On Wed, Aug 17, 2022 at 9:31 AM Jaroslaw via bitcoin-dev <
bitcoin-dev@lists.linuxfoundation.org> wrote:

>
> On one scale you puts the Trust to the large stakeholders (why we avoid
> plenty of small stakeholders, btw),
> and on the other side I put game theory and well defined Prisoner's
> Dilemma.
>
> Again: large stakeholders WILL NOT incentivised to mine, they will have
> the hundreds excuses why not to switch-on Antminers back.
> That's how it simply works.  Bitcoin would fail miserably if Satoshi was
> based his concept mainly on existence of idealists.
>
> If we will observe lack of hashrate recovery four years after some halving
> and still unprepared like today
> - means the trust in large stakeholders was a very costly mistake.
>
>
> Superiority of Proof of Work against Proof of Stake has been discussed
> enough either
> The overall conclusion with what I fully agree  is: swapping PoW to PoS -
> would be a degradation.
> You can stop talking about degradation to proof of stake, but just:
> degradation.
>
> Degradation of Bitcoin, due to human greed.
>
> Now you mine and you have an INSTANT gratification.
> Then you will mine and it will cost you real money, but simple switch -
> and you have a DELAYED, maybe some day in the future, maybe only a tiny -
> punishment.
> And The Punishment Won't Be Tiny.
>
>
> "If the pain after hitting the hand with a hammer would appear after a
> month - people would notoriously walk with swollen fingers"
> 100% (^2)
>
> Regards
> Jaroslaw
>
>
>
> W dniu 2022-08-17 13:10:38 użytkownik Erik Aronesty <erik@q32.com>
> napisał:
>
> > you can stop talking about  the "security of the system" as meaningful
> > this has been discussed enough
> > if fees are not sufficient, clearance times increase and large
> stakeholders are incentivised to mine
> > in the best case, fees are sufficient
> > in the worst case, it degrades to proof of stake
> > i'm sure you can see how that's fine either way
>
>
>
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>
>
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Breno Brito]

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Since we are talking about inflation and Milton Friedman, this Friedman's
interview seems relevant.
[image: image.png]
Source:
https://www.econlib.org/library/Columns/y2006/Friedmantranscript.html

Regards,
Breno Brito


On Wed, Aug 17, 2022 at 11:31 AM Jaroslaw via bitcoin-dev <
bitcoin-dev@lists.linuxfoundation.org> wrote:

>
> On one scale you puts the Trust to the large stakeholders (why we avoid
> plenty of small stakeholders, btw),
> and on the other side I put game theory and well defined Prisoner's
> Dilemma.
>
> Again: large stakeholders WILL NOT incentivised to mine, they will have
> the hundreds excuses why not to switch-on Antminers back.
> That's how it simply works.  Bitcoin would fail miserably if Satoshi was
> based his concept mainly on existence of idealists.
>
> If we will observe lack of hashrate recovery four years after some halving
> and still unprepared like today
> - means the trust in large stakeholders was a very costly mistake.
>
>
> Superiority of Proof of Work against Proof of Stake has been discussed
> enough either
> The overall conclusion with what I fully agree  is: swapping PoW to PoS -
> would be a degradation.
> You can stop talking about degradation to proof of stake, but just:
> degradation.
>
> Degradation of Bitcoin, due to human greed.
>
> Now you mine and you have an INSTANT gratification.
> Then you will mine and it will cost you real money, but simple switch -
> and you have a DELAYED, maybe some day in the future, maybe only a tiny -
> punishment.
> And The Punishment Won't Be Tiny.
>
>
> "If the pain after hitting the hand with a hammer would appear after a
> month - people would notoriously walk with swollen fingers"
> 100% (^2)
>
> Regards
> Jaroslaw
>
>
>
> W dniu 2022-08-17 13:10:38 użytkownik Erik Aronesty <erik@q32.com>
> napisał:
>
> > you can stop talking about  the "security of the system" as meaningful
> > this has been discussed enough
> > if fees are not sufficient, clearance times increase and large
> stakeholders are incentivised to mine
> > in the best case, fees are sufficient
> > in the worst case, it degrades to proof of stake
> > i'm sure you can see how that's fine either way
>
>
>
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>
>
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[jk_14]

On one scale you puts the Trust to the large stakeholders (why we avoid plenty of small stakeholders, btw),
and on the other side I put game theory and well defined Prisoner's Dilemma.

Again: large stakeholders WILL NOT incentivised to mine, they will have the hundreds excuses why not to switch-on Antminers back.
That's how it simply works.  Bitcoin would fail miserably if Satoshi was based his concept mainly on existence of idealists.

If we will observe lack of hashrate recovery four years after some halving and still unprepared like today
- means the trust in large stakeholders was a very costly mistake.


Superiority of Proof of Work against Proof of Stake has been discussed enough either
The overall conclusion with what I fully agree  is: swapping PoW to PoS - would be a degradation.
You can stop talking about degradation to proof of stake, but just: degradation.

Degradation of Bitcoin, due to human greed.

Now you mine and you have an INSTANT gratification.
Then you will mine and it will cost you real money, but simple switch - and you have a DELAYED, maybe some day in the future, maybe only a tiny - punishment.
And The Punishment Won't Be Tiny.


"If the pain after hitting the hand with a hammer would appear after a month - people would notoriously walk with swollen fingers"
100% (^2)

Regards
Jaroslaw



W dniu 2022-08-17 13:10:38 użytkownik Erik Aronesty <erik@q32.com> napisał:

> you can stop talking about  the "security of the system" as meaningful
> this has been discussed enough
> if fees are not sufficient, clearance times increase and large stakeholders are incentivised to mine 
> in the best case, fees are sufficient
> in the worst case, it degrades to proof of stake
> i'm sure you can see how that's fine either way



_______________________________________________
bitcoin-dev mailing list
bitcoin-dev@lists.linuxfoundation.org
https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev


_______________________________________________
bitcoin-dev mailing list
bitcoin-dev@lists.linuxfoundation.org
https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev

Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Erik Aronesty]

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you can stop talking about  the "security of the system" as meaningful

this has been discussed enough

if fees are not sufficient, clearance times increase and large stakeholders
are incentivised to mine

in the best case, fees are sufficient

in the worst case, it degrades to proof of stake

i'm sure you can see how that's fine either way


On Mon, Aug 15, 2022 at 9:59 PM Jaroslaw via bitcoin-dev <
bitcoin-dev@lists.linuxfoundation.org> wrote:

>
> > New blog post:
> >
> https://petertodd.org/2022/surprisingly-tail-emission-is-not-inflationary
>
>
> Tail emission is inevitable, Milton Friedman says...
>
>
> The key thing here in my opinion is to properly understand the seriousness
> of the situation.
> "There is no such thing as a free lunch" - is definitely helpful quote
> here.
>
> There are two edge cases.
>
> 1. while starting given cryptocurrency
> - the annual inflation is huge, nobody (in developed/mature monetary
> system) would like to keep such kind of money with e.g. 100% annual
> inflation rate, but from the other side there is no problem for transaction
> fee to be free of charge here
>
> 2. while given cryptocurrency is switching off the block reward, in
> supposed "mature phase":
> - the annual inflation is zero, everyone want to hoard such money,
> transaction fees must carry the whole security of the system
>
>
> In the first edge case: active users have got "free lunches" and passive
> users (i.e. holders) are paying for it (by "inflation tax")
> In the second edge case: passive users have got "free lunches" and active
> users should pay for it (by "transactional tax")
>
> So far I only highlighted some maybe not very well recognized, but pure
> facts (it's not comfortable to contradict the facts...)
>
>
> The reason people do pay in the first phase - is a hope/promise of system
> growth (future coin price appreciation = profit)
> The problem in the second phase is that there is no real incentive for
> people to pay for other's free lunches.
>
>
> Any wishful thinking that most (or even: any significant part) of holders
> will resign from a free lunch and will buy and run ASIC mining equipment at
> loss - is just a delusional perspective. It's well proven by game theory
> and what says us the Prisoner's Dilemma about it. For better understanding
> - here is my modified version of Prisoner's Dilemma short description:
>
> "The Prisoner's Dilemma is a standard example of a game analyzed in game
> theory that shows why completely rational large holders might not
> cooperate, even if it appears that it is in their best interests to do so."
>
> I'm pretty sure we will have a textbook case of Prisoner's Dilemma here.
>
> As a useful example - let's assume that fees don't compensate low block
> reward. Btw, right now a single transaction fee need to be $60 to
> compensate that (and it will only get worse in time). System is not
> inclusive with $60 per transaction fee. Only rich people will use it.
> Another possible scenario is a x100 drop of network hashrate to catch a
> previous fee levels. The network is x100 less secure, then. It really
> doesn't matter if this process is spread over the long run...
>
> So, for example - let every 10 BTC holding needs to be secured by one
> Antminer S19 running.
>
> In an ideal world every large bitcoin holder will run proper amount of
> ASICs and run it at loss.
> The holders of less than 10 BTC - will organize "group pays", this time
> for sharing loss (electricity costs)
> Exactly the same way like people made "group buys" of ASIC hardware in
> 2013.
>
> I hope it's clear that in the real world it WILL NOT work. People will
> simply think, that there is only a tiny punishment for betrayal.
> Noone will waste his renewable energy on unprofitable Antminer while
> he/she can sell this energy for the market price. Even Bitcoin can't beat
> the human nature.
>
>
> Thanks to Milton Friedman - we can easily say that situation with "free
> lunches" (at least for some part of users) - is an unhealthy state of
> financial system.
> And may last only exceptionally for short period of time, and definitely
> not as a default state. System must be sustainable and time to accept that
> there is a real problem here (or: an elephant in the room - but maybe not
> such invisible like was before).
>
> The good news is a natural solution exists. Bitcoin can solve this issue
> natural way.
>
> While decreasing block reward and moving from the first edge case to the
> second one - the system naturally cross the Area of Balance.
> And healthy system should stay somewhere in such area. And that's exactly
> what Monero did. But they did it arbitrally, at 0.9% level.
> Bitcoin is able to do it much better - because empirically.
>
> There is a simple trigger if the system is leaving an Area of Balance and
> cross the line of Phase 2 with "free lunches". The network difficulty /
> global network hashrate chart.
> Four years after some particular halving (in 2028, 2032 or later - no
> matter when in fact) - we will (definitely) see difficulty is not recovered
> during four long years.
> This is a big red light. It means that halvings starts to be destructive
> to the network security.
>
> Something what became destructive to the network - must be removed.
> Halving must be removed in such moment. Moment determined empirically -
> what is good thing. Satoshi Nakamoto wasn't able to properly predict when
> this moment may appear, but we are in better situation.
>
> "Bitcoin to the moon" (and any other pro-21M hardcap shortsighted slogans)
> - must have a lower priority than network security/health.
> I'm sure Satoshi would agree with it. Of course, someone may set up such
> environment, where holders (i.e. passive users) have got a free lunches
> and security of network is based on active users' shoulders only. Someone
> could even insist that it is quite fair...
> But please don't expect a lack of impact for the network security where
> not all, but only a part of users - participate in supporting network
> health.
> Many people don't realise a simple fact: keeping destructive halvings in
> such situation above, just for maximising appreciation of already hoarded
> coins
> - is counterproductive. Because the network security is decreasing.
>
>
> We have a lot of time yet to educate people about it - for reaching common
> consensus for halvings removal with "ease".
> We should probably use Milton Friedman's quote and highlight that balanced
> system with 0.45% / 0.225% / 0.1125% (?) annual inflation rate (and slowly
> decreasing)
> - is still enormously better than any surrounding fiat system. But system
> still balanced and stable - and not in spiral of death...
>
>
> “Bitcoin should have had a 0.1% or 1% monetary inflation tax to pay for
> security,” Peter said long time ago, further arguing bitcoin will die if it
> doesn’t change the limit.
>
> I fully agree with Peter. The halvings should be removed in case it starts
> to be destructive to the network security (lack of hashrate recovery during
> long 4 years after given halving). Because that means bitcoin system has
> reached equilibrium / saturation on a globe scale level. The evolutionary
> path is the best path.
> The worst path is: overcomplicated constructs, completely unclear for
> Average Joe. Additional merge-mining coins, whatever etc. - just to achieve
> the same final goal.
> KISS = Keep It Simple. Halving removal is the most honest, simplest and
> most understandable way to make every bitcoin pasive user to participate in
> keeping Bitcoin network secure. It just force the rule, that someone pay
> proportionally to amount of bitcoins he/she hold, and all participants are
> sure that everybody participate (no Prisoner's Dilemma, what is crucial
> matter)
>
>
> Yes, that means: hard fork. But as written above - Bitcoin will die
> without the solution.
>
> Bitcoin may be also out of sudden in a deadly risk from quantum computers.
> In such circumstances everyone (or: almost, i.e. everyone who cares) -
> would immediately download a quantum resistant, freshly released bitcoin
> wallet, no doubt. And these two dangers are similar at least in one aspect:
> both will cause the spiral of death.
> Widespread consensus would be the best scenario, but from the other side:
> a fork always shows retrospectively, who was right (BCH turmoil in 2017)
>
>
> Regards
> Jaroslaw
>
>
> P.S  some other resources yet:
>
> "Friedman originally proposed a fixed monetary rule, called Friedman's
> k-percent rule, where the money supply would be automatically increased by
> a fixed percentage per year. Under this rule, there would be no leeway for
> the central reserve bank, as money supply increases could be determined "by
> a computer", and business could anticipate all money supply changes. With
> other monetarists he believed that the active manipulation of the money
> supply or its growth rate is more likely to destabilise than stabilise the
> economy.
>
> Most monetarists oppose the gold standard. Friedman, for example, viewed a
> pure gold standard as impractical.[9] For example, whereas one of the
> benefits of the gold standard is that the intrinsic limitations to the
> growth of the money supply by the use of gold would prevent inflation, if
> the growth of population or increase in trade outpaces the money supply,
> there would be no way to counteract deflation and reduced liquidity (and
> any attendant recession) except for the mining of more gold"
>
> no block reward  => reduced liquidity (reduced number of transactions) =>
> network security in spiral of death
>
> https://en.wikipedia.org/wiki/Monetarism
> https://en.wikipedia.org/wiki/Friedman%27s_k-percent_rule
> https://twitter.com/hasufl/status/1511470668457652224
>
>
>
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>
>
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[jk_14]

Hi, Peter

Thanks to human nature, still:

1. Bitcoin large holders are able to communicate with each other...
- and as a large bitcoin holder someone will very well understand that he should run his Antminers at loss for goodness of Bitcoin network security.
But he won't communicate that - due to his greed - he just betrayed it. Maybe someone will communicate that he is running Anminers... But it doesn't change a lot.
We can assume this additional possibility of communication (especially taking into account big number of large holders and their anonimity) - doesn't change this Prisoner's Dilemma into a "not textbook case enough".

2. The existing incentive that miners earn money for including transactions is enough to motivate human nature...
- but paying $50 usd per such transaction (the amount necessary to compensate lack of block reward right now) - is "no way" to motivate a human nature, just due to: personal interest (as you correctly highlighted). It really doesn't matter that the process of disappearance of block reward is spreaded over the long run.
(the same, but more terse: https://twitter.com/hasufl/status/1511470668457652224 )

3. In many jurisdictions you can take back from grid for free - the amount you have produced and uploaded earlier (I'm in one of such). So I won't invest and oversize my solar panels by additional ~24kW of power for additional Antminer runing 24h/day - if I know it will be running at loss. (side note: it's not a good idea to be dependant with future health of bitcoin -  on what type of jurisdiction is the most popular one in given moment)


There are two statements to repeat then, but more precisely:

A. Bitcoiners (me too) are proud the bitcoin system is designed so clever, that from the beginning till now - is able to run without the trust to anyone. And utilise even people's greed - for system goodness/expansion. But when I wrote the FIRST edge case is behind us, but the SECOND one - with no doubt with pathological Friedman's "free lunches" for part of participants - is only some years ahead (like in a Titanic scene) - then most of them suddenly say:

"Ok, then... Bitcoin idea is so brilliant that maybe the game theory won't apply anymore. Let's TRUST the large holders they will run Antminers at loss."

It's not The Satoshi's Vision anymore.


B. Bitcoiners (me too) want to remove or neutralise all destructive things to Bitcoin, like for example: unfriendly government regulations, etc. But when I wrote there will be in the future (and the only question is: when) an alarm siren that halvings start to be destructive to the Bitcoin network, while start to cause consecutive network security/hashrate regressions - then most of them suddenly say:

"Ok, then... I'm to greed to resign from it."



It's not The Satoshi's Vision anymore.

Regards
Jaroslaw




W dniu 2022-08-16 23:21:30 użytkownik Peter via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org> napisał:
Hi Jaroslaw,

In the Prisoner's Dilemma the prisoners cannot communicate. In Bitcoin large holders are able to communicate with each other. Also, prisoners need not make an all or nothing decision in Bitcoin. Miners can join and leave the network freely over time. You can change your decision based on the decision of others.

The Bitcoin design is such that security is volatile but the issuance of blocks is timely and evened out to a 10 minutes average even after the reward is exhausted.

The existing incentive that miners earn money for including transactions is enough to motivate human nature. Transaction initiators have an incentive to mine and run full nodes for personal interest.

>Noone will waste his renewable energy on unprofitable Antminer while he/she can sell this energy for the market price.

The law in most jurisdictions prevents the resale of spare electricity unless an expensive license is obtained (and in most cases no license is available as the government maintains a monopoly). Mining with waste electricity is reducing losses. Another incentive to motivate human nature.

Bitcoin holders can be enfranchised into any new system. So, no need for bike shedding the original design which is a Schelling Point.

Regards

Peter Kroll

pointbiz/ BTCCuracao

Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Peter]

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Hi Jaroslaw,

In the Prisoner's Dilemma the prisoners cannot communicate. In Bitcoin large holders are able to communicate with each other. Also, prisoners need not make an all or nothing decision in Bitcoin. Miners can join and leave the network freely over time. You can change your decision based on the decision of others.

The Bitcoin design is such that security is volatile but the issuance of blocks is timely and evened out to a 10 minutes average even after the reward is exhausted.

The existing incentive that miners earn money for including transactions is enough to motivate human nature. Transaction initiators have an incentive to mine and run full nodes for personal interest.

>Noone will waste his renewable energy on unprofitable Antminer while he/she can sell this energy for the market price.

The law in most jurisdictions prevents the resale of spare electricity unless an expensive license is obtained (and in most cases no license is available as the government maintains a monopoly). Mining with waste electricity is reducing losses. Another incentive to motivate human nature.

Bitcoin holders can be enfranchised into any new system. So, no need for bike shedding the original design which is a Schelling Point.

Regards

Peter Kroll

pointbiz/ BTCCuracao

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[jk_14]

> New blog post:
> https://petertodd.org/2022/surprisingly-tail-emission-is-not-inflationary


Tail emission is inevitable, Milton Friedman says...


The key thing here in my opinion is to properly understand the seriousness of the situation.
"There is no such thing as a free lunch" - is definitely helpful quote here.

There are two edge cases.

1. while starting given cryptocurrency
- the annual inflation is huge, nobody (in developed/mature monetary system) would like to keep such kind of money with e.g. 100% annual inflation rate, but from the other side there is no problem for transaction fee to be free of charge here

2. while given cryptocurrency is switching off the block reward, in supposed "mature phase":
- the annual inflation is zero, everyone want to hoard such money, transaction fees must carry the whole security of the system


In the first edge case: active users have got "free lunches" and passive users (i.e. holders) are paying for it (by "inflation tax")
In the second edge case: passive users have got "free lunches" and active users should pay for it (by "transactional tax")

So far I only highlighted some maybe not very well recognized, but pure facts (it's not comfortable to contradict the facts...)


The reason people do pay in the first phase - is a hope/promise of system growth (future coin price appreciation = profit)
The problem in the second phase is that there is no real incentive for people to pay for other's free lunches.


Any wishful thinking that most (or even: any significant part) of holders will resign from a free lunch and will buy and run ASIC mining equipment at loss - is just a delusional perspective. It's well proven by game theory and what says us the Prisoner's Dilemma about it. For better understanding - here is my modified version of Prisoner's Dilemma short description:

"The Prisoner's Dilemma is a standard example of a game analyzed in game theory that shows why completely rational large holders might not cooperate, even if it appears that it is in their best interests to do so."

I'm pretty sure we will have a textbook case of Prisoner's Dilemma here.

As a useful example - let's assume that fees don't compensate low block reward. Btw, right now a single transaction fee need to be $60 to compensate that (and it will only get worse in time). System is not inclusive with $60 per transaction fee. Only rich people will use it. Another possible scenario is a x100 drop of network hashrate to catch a previous fee levels. The network is x100 less secure, then. It really doesn't matter if this process is spread over the long run...

So, for example - let every 10 BTC holding needs to be secured by one Antminer S19 running.

In an ideal world every large bitcoin holder will run proper amount of ASICs and run it at loss.
The holders of less than 10 BTC - will organize "group pays", this time for sharing loss (electricity costs)
Exactly the same way like people made "group buys" of ASIC hardware in 2013.

I hope it's clear that in the real world it WILL NOT work. People will simply think, that there is only a tiny punishment for betrayal.
Noone will waste his renewable energy on unprofitable Antminer while he/she can sell this energy for the market price. Even Bitcoin can't beat the human nature.


Thanks to Milton Friedman - we can easily say that situation with "free lunches" (at least for some part of users) - is an unhealthy state of financial system.
And may last only exceptionally for short period of time, and definitely not as a default state. System must be sustainable and time to accept that there is a real problem here (or: an elephant in the room - but maybe not such invisible like was before).

The good news is a natural solution exists. Bitcoin can solve this issue natural way.

While decreasing block reward and moving from the first edge case to the second one - the system naturally cross the Area of Balance.
And healthy system should stay somewhere in such area. And that's exactly what Monero did. But they did it arbitrally, at 0.9% level.
Bitcoin is able to do it much better - because empirically.

There is a simple trigger if the system is leaving an Area of Balance and cross the line of Phase 2 with "free lunches". The network difficulty / global network hashrate chart.
Four years after some particular halving (in 2028, 2032 or later - no matter when in fact) - we will (definitely) see difficulty is not recovered during four long years.
This is a big red light. It means that halvings starts to be destructive to the network security. 

Something what became destructive to the network - must be removed. Halving must be removed in such moment. Moment determined empirically - what is good thing. Satoshi Nakamoto wasn't able to properly predict when this moment may appear, but we are in better situation.

"Bitcoin to the moon" (and any other pro-21M hardcap shortsighted slogans) - must have a lower priority than network security/health.
I'm sure Satoshi would agree with it. Of course, someone may set up such environment, where holders (i.e. passive users) have got a free lunches
and security of network is based on active users' shoulders only. Someone could even insist that it is quite fair...
But please don't expect a lack of impact for the network security where not all, but only a part of users - participate in supporting network health.
Many people don't realise a simple fact: keeping destructive halvings in such situation above, just for maximising appreciation of already hoarded coins
- is counterproductive. Because the network security is decreasing.


We have a lot of time yet to educate people about it - for reaching common consensus for halvings removal with "ease".
We should probably use Milton Friedman's quote and highlight that balanced system with 0.45% / 0.225% / 0.1125% (?) annual inflation rate (and slowly decreasing)
- is still enormously better than any surrounding fiat system. But system still balanced and stable - and not in spiral of death...


“Bitcoin should have had a 0.1% or 1% monetary inflation tax to pay for security,” Peter said long time ago, further arguing bitcoin will die if it doesn’t change the limit.

I fully agree with Peter. The halvings should be removed in case it starts to be destructive to the network security (lack of hashrate recovery during long 4 years after given halving). Because that means bitcoin system has reached equilibrium / saturation on a globe scale level. The evolutionary path is the best path.
The worst path is: overcomplicated constructs, completely unclear for Average Joe. Additional merge-mining coins, whatever etc. - just to achieve the same final goal.
KISS = Keep It Simple. Halving removal is the most honest, simplest and most understandable way to make every bitcoin pasive user to participate in keeping Bitcoin network secure. It just force the rule, that someone pay proportionally to amount of bitcoins he/she hold, and all participants are sure that everybody participate (no Prisoner's Dilemma, what is crucial matter)


Yes, that means: hard fork. But as written above - Bitcoin will die without the solution.

Bitcoin may be also out of sudden in a deadly risk from quantum computers. In such circumstances everyone (or: almost, i.e. everyone who cares) - would immediately download a quantum resistant, freshly released bitcoin wallet, no doubt. And these two dangers are similar at least in one aspect: both will cause the spiral of death.
Widespread consensus would be the best scenario, but from the other side: a fork always shows retrospectively, who was right (BCH turmoil in 2017)


Regards
Jaroslaw


P.S  some other resources yet:

"Friedman originally proposed a fixed monetary rule, called Friedman's k-percent rule, where the money supply would be automatically increased by a fixed percentage per year. Under this rule, there would be no leeway for the central reserve bank, as money supply increases could be determined "by a computer", and business could anticipate all money supply changes. With other monetarists he believed that the active manipulation of the money supply or its growth rate is more likely to destabilise than stabilise the economy.

Most monetarists oppose the gold standard. Friedman, for example, viewed a pure gold standard as impractical.[9] For example, whereas one of the benefits of the gold standard is that the intrinsic limitations to the growth of the money supply by the use of gold would prevent inflation, if the growth of population or increase in trade outpaces the money supply, there would be no way to counteract deflation and reduced liquidity (and any attendant recession) except for the mining of more gold"

no block reward  => reduced liquidity (reduced number of transactions) => network security in spiral of death

https://en.wikipedia.org/wiki/Monetarism
https://en.wikipedia.org/wiki/Friedman%27s_k-percent_rule
https://twitter.com/hasufl/status/1511470668457652224



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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[jk_14]

Let's assume fees don't compensate low block reward.
And for example every 10 BTC holding needs to be secured by one Antminer S19 running.

In an ideal world every large bitcoin holder will run proper amount of ASICs and run it at loss.
The holders of less than 10 BTC - will organize "group pays", this time for sharing loss (electricity costs)
(exactly the same way like people made "group buys" of ASIC hardware in 2013)


Pretty sure in real world it won't work. And there is a large payoff for betrayal, or more precise:
People will think there is tiny punishment for betrayal.

Even Bitcoin can't beat a human nature.


Regards
Jaroslaw


W dniu 2022-07-26 19:06:12 użytkownik Erik Aronesty <erik@q32.com> napisał:
> I'm pretty sure we will have a textbook case of Prisoner's Dilemma here.


no, there is no large payoff for betrayal

Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Erik Aronesty]

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> I'm pretty sure we will have a textbook case of Prisoner's Dilemma here.

no, there is no large payoff for betrayal

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[jk_14]

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"large holders who perform zero transactions will still mine in order to preserve the value of the network"
let me slightly modify the sentence below:
"The Prisoner's Dilemma is a standard example of a game analyzed in game theory that shows why completely rational large holders might not cooperate, even if it appears that it is in their best interests to do so."
I'm pretty sure we will have a textbook case of Prisoner's Dilemma here.
Regards
Jaroslaw
W dniu 2022-07-26 10:20:38 użytkownik Erik Aronesty via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org> napisał:
even with zero block reward and minimal fees, large holders who perform zero transactions will still mine in order to preserve the value of the network
 
this is not "mining your own tx", it is unrelated
 
this is "mining at a small loss to preserve your stake"
 
not only don't we need issuance or fees, but also the censorship resistance is not meaningfully improved with issuance 
 
On Mon, Jul 18, 2022 at 3:14 PM Erik Aronesty <erik@q32.com> wrote:
subsidy to directly tie miner revenue to the total value of Bitcoin
makes it not exactly how we want to incentivise a service that keeps
 
again, this is meaningless.   if the fees aren't enough to keep  bitcoin secure for large transactions, then large holders are incentivised to mine
 
that's it.
 
it's not complicated

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Erik Aronesty]

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even with zero block reward and minimal fees, large holders who perform
zero transactions will still mine in order to preserve the value of the
network

this is not "mining your own tx", it is unrelated

this is "mining at a small loss to preserve your stake"

not only don't we need issuance or fees, but also the censorship resistance
is not meaningfully improved with issuance


On Mon, Jul 18, 2022 at 3:14 PM Erik Aronesty <erik@q32.com> wrote:

>
>> subsidy to directly tie miner revenue to the total value of Bitcoin
>> makes it not exactly how we want to incentivise a service that keeps
>>
>>
> again, this is meaningless.   if the fees aren't enough to keep  bitcoin
> secure for large transactions, then large holders are incentivised to mine
>
> that's it.
>
> it's not complicated
>

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Eric Voskuil]

If there’s no block reward, there’s no Bitcoin, so that’s moot. But setting that aside. The business model of the state is to preserve the reward it obtains from its own money. This is the reason for currency controls, which are common.

e

> On Jul 20, 2022, at 03:17, Peter via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org> wrote:
> 
> >And therefore this reduces to the simple fact that tx fees are what provides censorship resistance, whether you mine your own or others?.
> 
> 
> What's the business model of the person who mines with the intention to censor transactions when there's no block reward?
> 
> 
> 
> Regards
> 
> Peter Kroll
> 
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev

Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Peter]

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>And therefore this reduces to the simple fact that tx fees are what provides censorship resistance, whether you mine your own or others?.

What's the business model of the person who mines with the intention to censor transactions when there's no block reward?

Regards

Peter Kroll

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Eric Voskuil]

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> On Jul 18, 2022, at 14:14, Erik Aronesty via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org> wrote:
> 
> 
>> 
>> subsidy to directly tie miner revenue to the total value of Bitcoin 
>> makes it not exactly how we want to incentivise a service that keeps 
>> 
> 
> again, this is meaningless.   if the fees aren't enough to keep  bitcoin secure for large transactions, then large holders are incentivised to mine

Yes, this is another way to pay the tx fee - you mine at cost sufficient to overpower the censor. You are spending the block reward in getting your txs confirmed, and that’s your fee.

But unless you are mining full blocks of only your own transactions, this implies that you are accepting these higher fees on censored txs from others. Otherwise you are simply mining at a loss, which we cannot use as a rational basis for security.

And therefore this reduces to the simple fact that tx fees are what provides censorship resistance, whether you mine your own or others’.

e

> that's it.
> 
> it's not complicated
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Erik Aronesty]

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>
>
> subsidy to directly tie miner revenue to the total value of Bitcoin
> makes it not exactly how we want to incentivise a service that keeps
>
>
again, this is meaningless.   if the fees aren't enough to keep  bitcoin
secure for large transactions, then large holders are incentivised to mine

that's it.

it's not complicated

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[David A. Harding]

On 2022-07-10 07:27, Peter Todd via bitcoin-dev wrote:
> The block subsidy directly ties miner revenue to the total value of 
> Bitcoin:
> that's exactly how you want to incentivise a service that keeps Bitcoin 
> secure.

I'm confused.  I thought your argument in the OP of this thread was that 
a perpetual block subsidy would *not* be tied to the total value of 
bitcoin.  It'd be tied to the total value of bitcoin *lost* each year on 
average.

If so, would you then agree that the inability of a perpetual block 
subsidy to directly tie miner revenue to the total value of Bitcoin 
makes it not exactly how we want to incentivise a service that keeps 
Bitcoin secure?

Thanks,

-Dave

Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Zac Greenwood]

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> your proof is incorrect (or, rather, relies on a highly unrealistic
assumption)

The assumption that coin are lost ar a constant rate is not required. Tail
emission will asymptotically decrease the rate of inflation to zero, at
which point the increase in coin exactly matches the amount of coin lost.
The rate at which coin are lost is irrelevant.

This is easy to see. Consider no coin are ever lost. The rate of inflation
will slowly decline to zero as the amount of coin grows to infinity.
However, lost coin ensures that the point at which the rate of inflation
becomes zero will be reached sooner.

If a black swan event destroys 90% of all coin, the constant tail emission
will instantly begin to inflate the supply at a 10x higher percentage. The
inflation expressed as a percentage will also immediately start to decline
because each new coin will inflate the total supply with a slightly smaller
percentage than the previous new coin. The rate of inflation will continue
to decline until zero, at which point it again matches the coin-loss
induced deflation rate.

Another scenario. Suppose that the number of coin lost becomes
significantly less for instance because better wallets and a more mature
ecosystem prevent many common coin loss events. A constant issuance of new
coin would increase the total supply, but each new coin would add less to
the total supply when expressed as a percentage. The rate of inflation
would decline to zero, at which point it again has matched the rate of
deflation due to coin loss.

Even when the rate at which coin are lost will not be constant, a tail
emission will tend to an equilibrium.

It must be observed that tail emission causes the total *potential* supply
to vary greatly depending on the deflation rate. In a low-deflation
scenario, the supply will have to grow much larger before an equilibrium
can be reached than in a scenario with moderate deflation rate. Not being
able to predict the ultimate total supply of coin is however seems
undesirable. But is it really?

The rate of inflation required for keeping Bitcoin useful highly depends on
the value of the token. At US$100k, a tail emission of 1 BTC per block
ensures safety within a few blocks for even large amounts. Continuing this
example, 1 BTC per block would mean 5.25m extra coin per 100 years. At 21m
coins and 1 BTC perpetual reward per block, the rate of inflation would be
0.25% per year.

This should put things a bit into perspective.


On Tue, 12 Jul 2022 at 01:58, Anthony Towns via bitcoin-dev <
bitcoin-dev@lists.linuxfoundation.org> wrote:

> On Mon, Jul 11, 2022 at 08:56:04AM -0400, Erik Aronesty via bitcoin-dev
> wrote:
> > > Alternatively, losses could be at a predictable rate that's entirely
> > > different to the one Peter assumes.
> > No, peter only assumes that there *is* a rate.
>
> No, he assumes it's a constant rate. His integration step gives a
> different result if lambda changes with t:
> https://www.wolframalpha.com/input?i=dN%2Fdt+%3D+k+-+lambda%28t%29*N
>
> On Mon, Jul 11, 2022 at 12:59:53PM -0400, Peter Todd via bitcoin-dev wrote:
> > Give me an example of an *actual* inflation rate you expect to see,
> given a
> > disaster of a given magnitude.
>
> All I was doing was saying your proof is incorrect (or, rather, relies
> on a highly unrealistic assumption), since I hadn't seen anybody else
> point that out already.
>
> But even if the proof were correct, I don't think it provides a useful
> mechanism (since there's no reason to think miners gaining all the coins
> lost in a year will be sufficient for anything), and I don't really
> think the "security budget" framework (ie, that the percentage of total
> supply given to miners each year is what's important for security)
> you're implicitly relying on is particularly meaningful.
>
> So no, not particularly interested in diving into it any deeper.
>
> Cheers,
> aj
>
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Alfred Hodler]

Rather than get bogged down discussing the technical details of how such a change could even take place, I'll go ahead and say that modifying the 21M cap is a supremely reckless idea. Your mathematical proof aside, the idea rests on the unprovable premise that people will keep losing coins indefinitely. You could also argue that once Bitcoin is valuable or widespread enough, it'll incentivize the creation of superior storage, custody and inheritance solutions. One could also write a bunch of "proofs" to support that, but it doesn't mean much when the core idea remains purely in the hypothetical sphere.

One of Bitcoin's value propositions is having a fixed supply cap with a predictable issuance curve. People bought into Bitcoin because it promises to NOT be fiat and because it promises NOT to do what central banks are doing. The moment you start messing with that, it'll invite people to try to tinker with the protocol whenever "security" concerns demand it. Once a powerful enough adversary sees that Overton window moving, they'll probably throw everything they have at this particular weakness in an attempt to subvert the protocol further.

Alfred

Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Anthony Towns]

On Mon, Jul 11, 2022 at 08:56:04AM -0400, Erik Aronesty via bitcoin-dev wrote:
> > Alternatively, losses could be at a predictable rate that's entirely
> > different to the one Peter assumes.
> No, peter only assumes that there *is* a rate.

No, he assumes it's a constant rate. His integration step gives a
different result if lambda changes with t:
https://www.wolframalpha.com/input?i=dN%2Fdt+%3D+k+-+lambda%28t%29*N

On Mon, Jul 11, 2022 at 12:59:53PM -0400, Peter Todd via bitcoin-dev wrote:
> Give me an example of an *actual* inflation rate you expect to see, given a
> disaster of a given magnitude.

All I was doing was saying your proof is incorrect (or, rather, relies
on a highly unrealistic assumption), since I hadn't seen anybody else
point that out already.

But even if the proof were correct, I don't think it provides a useful
mechanism (since there's no reason to think miners gaining all the coins
lost in a year will be sufficient for anything), and I don't really
think the "security budget" framework (ie, that the percentage of total
supply given to miners each year is what's important for security)
you're implicitly relying on is particularly meaningful.

So no, not particularly interested in diving into it any deeper.

Cheers,
aj

Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Dave Scotese]

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I believe it's foolish to attempt objective definitions of things that we
define collectively, like "Bitcoin."  The best any one of us can do is to
be consistent with a subjective personal definition.  I believe most people
do that with the term "Bitcoin" and that the capped supply is intrinsic to
their subjective definitions.  It is to mine.  Leading bodies, such as the
Bitcoin core team, the Ethereum foundation, and every government, are
constantly in danger of confusing objective reality with their own
decisions.  Since people have autonomy, the best a leading body can do is
recommend their decisions.  The common error is one made by governments,
where they react violently to defiance of the definitions they make.
Shadows of that error show up in nongovernmental leading bodies as
ostracism, criticism, and even sometimes illegal activity against such
defiance of decisions.  What I mean here is that John is right in a sense
(" removing this limit results in something that can no longer be called
Bitcoin.  "), but I don't think the way he expressed it is as helpful as it
could be.  There are many who will not call it Bitcoin, and I am among them.

On Sat, Jul 9, 2022 at 8:13 AM Peter Todd via bitcoin-dev <
bitcoin-dev@lists.linuxfoundation.org> wrote:

> On Sat, Jul 09, 2022 at 04:57:57PM +0200, John Tromp via bitcoin-dev wrote:
> > > New blog post:
> > >
> https://petertodd.org/2022/surprisingly-tail-emission-is-not-inflationary
> >
> > A Tail Emission is best described as disinflationary; the yearly
> > supply inflation steadily decreases toward zero.
>
> _Apparently_ inflation. True monetary inflation includes lost coins - both
> intentionally and accidentally lost. It's quite possible that even with
> tail
> emission Monero is currently a monetarily deflationary coin, as the lost
> coin
> rate might be higher than the 0.8% apparent tail emission rate.
>
> We just don't know. Doubly so in the case of monero where its privacy
> features
> hide coin activity.
>
> > > If an existing coin decides to implement tail emission as a means to
> fund security, choosing an appropriate emission rate is simple: decide on
> the maximum amount of inflation you are willing to have in the worst case,
> and set the tail emission accordingly.
> >
> > Any coin without a premine starts with infinite inflation. Bitcoin in
> > its first 4 years had yearly inflation rates of inf, 100%, 50%, and
> > 33%. So deciding on a maximum amount of inflation is deciding on a
> > premine.
>
> Hence why I specified an *existing* coin.
>
> > While in the long term, a capped supply doesn't meaningfully differ
> > from un uncapped supply [1], the 21M limit is central to Bitcoin's
> > identity, and removing this limit results in something that can no
> > longer be called Bitcoin.
>
> Personally I think basing your identity on a technical point that isn't
> even
> correct is stupid. And I suspect than when push comes to shove, if in ~10
> years
> or whatever Bitcoin turns out to be unstable without a reward, the market
> as a
> whole will be happy to redefine Bitcoin to remove the 21M limit. Whether
> or not
> it can do that fast enough to avoid Bitcoin dying first is an open
> question.
>
> --
> https://petertodd.org 'peter'[:-1]@petertodd.org
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>


-- 
I own Litmocracy <http://www.litmocracy.com> and Meme Racing
<http://www.memeracing.net> (in alpha).
I'm the webmaster for The Voluntaryist <http://www.voluntaryist.com> which
now accepts Bitcoin.
"He ought to find it more profitable to play by the rules" - Satoshi
Nakamoto

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Larry Ruane]

On Sun, Jul 10, 2022 at 3:05 AM vjudeu via bitcoin-dev
<bitcoin-dev@lists.linuxfoundation.org> wrote:
>
> Not really, because people that run full nodes, just accepted Segwit
> and Taproot. They had no choice. And in case of zero satoshis, it could
> be the same: you would see zero if you look at raw bytes, but you will
> see non-zero values, if you use some upgraded client, that will support
> amount hiding, or other features.
>
> Segwit: old nodes see no new signatures, new nodes see all signatures
> Zero satoshis: old nodes see new zero amounts, new nodes see all amounts
>
> It is that simple.

I see what you mean, have the P2P messages depend on whether the peer
is running old code (doesn't know about tail emission) or new code
(does know about it).

I don't think this can work in this case. It worked for Segwit because
the P2P differences involved only signatures (which determine whether
the transaction is valid), not the *effect* of the transaction, that is,
how it changes the UTXO set. Consensus requires all nodes to always
agree on the UTXO set.

Larry Ruane

Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Bram Cohen]

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On Mon, Jul 11, 2022 at 10:00 AM Peter Todd via bitcoin-dev <
bitcoin-dev@lists.linuxfoundation.org> wrote:

>
> If you actually do the numbers on this, you'll realize it takes absolutely
> catastrophic black swan events that make WW2 look like a minor conflict to
> make
> even insignificant inflation rate changes due to changes in lost coins.
>

That somewhat depends on what you mean by 'significant' and 'catastrophic'
but I believe the way the model goes is that if X% of coins are lost that
means that the value of all outstanding coins will go up by X%, and if the
rate of breakage goes from Y% annually to Y*Z% annually then the value of
all coins will go up by a factor of Z. This is of course an idealized model
in steady state, but gives some idea of scale.

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Peter Todd]

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On Mon, Jul 11, 2022 at 12:32:47PM +1000, Anthony Towns wrote:
> This isn't necessarily true: if the losses are due to a common cause,
> then they'll be heavily correlated rather than independent; for example
> losses could be caused by a bug in a popular wallet/exchange software
> that sends funds to invalid addresses, or by a war or natural disaster
> that damages key storage hardware. They're also not independent over
> time -- people improve their key storage habits over time; eg switching
> to less buggy wallets/exchanges, validating addresses before using them,
> using distributed multisig to prevent a localised disaster from being
> catastrophic.

People clearly continue to make downright irrational decisions about coin
security, doing things putting their entire crypto savings at risk for claimed
5% returns.

Even if people were rational, the coin loss rate would clearly reach a floor
because as the probability of coin loss goes down, bothering to spend extra
effort to decrease that already small chance is pointless. You mentioning black
swan events actually strengthens my point: at low coin loss rates the true loss
rate is dominated by black swan events. So it's pointless to go to extra effort
to prevent them.

Finally, you're forgetting that coin loss also includes *intentional* losses
from proof-of-sacrifice protocols. There are a number of examples on Bitcoin.
Again, they put a floor on how much coin loss could diminish.

> loss rate. If that's the case, then the rate at which funds are lost will
> vary chaotically, leading to "inflationary" periods in between events,
> and comparatively strong deflationary shocks when these events occur.

Give me an example of an *actual* inflation rate you expect to see, given a
disaster of a given magnitude.

If you actually do the numbers on this, you'll realize it takes absolutely
catastrophic black swan events that make WW2 look like a minor conflict to make
even insignificant inflation rate changes due to changes in lost coins.

-- 
https://petertodd.org 'peter'[:-1]@petertodd.org

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Erik Aronesty]

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>
>
> Alternatively, losses could be at a predictable rate that's entirely
> different to the one Peter assumes.
>

No, peter only assumes that there *is* a rate.

Regardless of what the rate is, if it is any value for which there exists
*any fixed central tendency*, tail emission is *evenually* non inflationary.

But you are correct about the other two things:

1. If people are improving custody faster than 1/(N(t)*P) than tail
emission can still be inflationary.  This seems far-fetched, imo.

2. The rate will be somewhat stochastic ("black swan envets").  Plausible
(popular wallet loses keys in coding error), but also... "true no matter
what".  And not really relevant to tail-emission  being non-inflationary.
 Over a long enough time period, even these events can be factored into a
fixed central tendency.   Even if it's 100 years, etc.

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Giuseppe B]

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I think the discussion has some anecdotic interest but has zero relevance
as far as any decision making is concerned.

Any extension of block rewards after the current deadline should only be
done if and only if the community agrees that it is the only way to keep
the network secure.

The fact that a mild inflation is sometimes compensated by coin loss is
like a bonus.

On Mon, Jul 11, 2022, 11:56 AM Stefan Richter via bitcoin-dev <
bitcoin-dev@lists.linuxfoundation.org> wrote:

> I very much agree with AJ here. This is something I remember discussing on
> Bitcointalk back in 2011: I find it highly intuitive that the amount of
> lost coins is not a constant fraction of the supply, because people get
> better at keeping their coins with increasing value, distribution and
> technology/best practices. I also think that we have observed this effect
> in practice since then. The bulk of coins that are supposed to be lost (via
> onchain analysis) haven't been moved since at least 2010. Of course, in
> most cases, we'll never know, but the assumption of constant loss rate
> seems unreasonable.
>
> Cheers
>   Stefan
>
> Anthony Towns via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org>
> schrieb am Mo., 11. Juli 2022, 04:32:
>
>> On Sat, Jul 09, 2022 at 08:46:47AM -0400, Peter Todd via bitcoin-dev
>> wrote:
>> > title:  "Surprisingly, Tail Emission Is Not Inflationary"
>>
>> > Of course, this isn't realistic as coins are constantly being lost due
>> to
>> > deaths, forgotten passphrases, boating accidents, etc. These losses are
>> > independent:
>>
>> This isn't necessarily true: if the losses are due to a common cause,
>> then they'll be heavily correlated rather than independent; for example
>> losses could be caused by a bug in a popular wallet/exchange software
>> that sends funds to invalid addresses, or by a war or natural disaster
>> that damages key storage hardware. They're also not independent over
>> time -- people improve their key storage habits over time; eg switching
>> to less buggy wallets/exchanges, validating addresses before using them,
>> using distributed multisig to prevent a localised disaster from being
>> catastrophic.
>>
>> > the *rate* of coin loss at time $$t$$ is
>> > proportional to the total supply *at that moment* in time.
>>
>> This is the key assumption that produces the claimed result.
>>
>> If you're losing a constant fraction, x (Peter's \lambda), of Bitcoins
>> each year, then as soon as the supply increases enough that the constant
>> reward, k, corresponds to the constant fraction, ie k = x*N(t), then
>> you've hit an equilibrium.  (Likewise if you're losing more than you're
>> increasing -- you just need to wait until N(t) decreases enough that you
>> reach the same equilibrium point) You don't really need any fancy maths.
>>
>> But that assumption doesn't need to be true; coins could primarily be
>> lost in "black swan" events (due to bugs, wars or disasters) rather
>> than at a predictable rate -- with actions taken thereafter such that
>> the same event repeating is no longer the same level of catastrophe,
>> but instead another new black swan event is required to maintain the same
>> loss rate. If that's the case, then the rate at which funds are lost will
>> vary chaotically, leading to "inflationary" periods in between events,
>> and comparatively strong deflationary shocks when these events occur.
>>
>> Alternatively, losses could be at a predictable rate that's entirely
>> different to the one Peter assumes.
>>
>> One alternative predictable rate that seems plausible to me is if funds
>> are lost due to people not be careful about losing small amounts; even
>> though they are careful when amounts are larger. So when 10k BTC was
>> worth $40, maybe it doesn't matter if you misplace a hard drive with
>> 7500 BTC on it since that's only worth $30; but by the time 7500 BTC
>> is worth $150M, maybe you take a bit more care with that, but are still
>> not too worried if you lose 1.5mBTC, since that's also only worth $30.
>>
>> To mathematise that, perhaps there are K people holding Bitcoin, and with
>> probability p, each loses $100 (in constant 2009 dollars say, so that we
>> can ignore inflation) of that Bitcoin a year through carelessness. For
>> an equilibrium to occur in that case, you need:
>>
>>   N(t) + k - (100/P * Kp) = N(t)
>>
>> where P is the price of Bitcoin (again in constant 2009 dollars) and k
>> is Peter's fixed tail subsidy. Simplifying gives:
>>
>>   P = K * 100p/k
>>
>> But k and p are constant by assumption in this scenario, so equilibrium
>> is reached only if price (P) is exactly proportional to number of
>> users (K). That requires you to have a non-inflationary currency
>> (supply is constant) with constant adoption (assume K doesn't change)
>> that maintains a constant price (P=K*100p/k) in real terms even if the
>> economy is otherwise expanding or contracting.
>>
>> More importantly, just from a goals point of view, x is something we
>> should be finding ways to minimise it over time, not leave constant.
>> In fact, you could argue for an even stronger goal: "the real value held
>> in BTC lost each year should decrease", that is, x should be decreasing
>> faster than 1/(N(t)*P).
>>
>> Cheers,
>> aj
>>
>> _______________________________________________
>> bitcoin-dev mailing list
>> bitcoin-dev@lists.linuxfoundation.org
>> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>>
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Stefan Richter]

[-- Attachment #1: Type: text/plain, Size: 4855 bytes --]

I very much agree with AJ here. This is something I remember discussing on
Bitcointalk back in 2011: I find it highly intuitive that the amount of
lost coins is not a constant fraction of the supply, because people get
better at keeping their coins with increasing value, distribution and
technology/best practices. I also think that we have observed this effect
in practice since then. The bulk of coins that are supposed to be lost (via
onchain analysis) haven't been moved since at least 2010. Of course, in
most cases, we'll never know, but the assumption of constant loss rate
seems unreasonable.

Cheers
  Stefan

Anthony Towns via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org>
schrieb am Mo., 11. Juli 2022, 04:32:

> On Sat, Jul 09, 2022 at 08:46:47AM -0400, Peter Todd via bitcoin-dev wrote:
> > title:  "Surprisingly, Tail Emission Is Not Inflationary"
>
> > Of course, this isn't realistic as coins are constantly being lost due to
> > deaths, forgotten passphrases, boating accidents, etc. These losses are
> > independent:
>
> This isn't necessarily true: if the losses are due to a common cause,
> then they'll be heavily correlated rather than independent; for example
> losses could be caused by a bug in a popular wallet/exchange software
> that sends funds to invalid addresses, or by a war or natural disaster
> that damages key storage hardware. They're also not independent over
> time -- people improve their key storage habits over time; eg switching
> to less buggy wallets/exchanges, validating addresses before using them,
> using distributed multisig to prevent a localised disaster from being
> catastrophic.
>
> > the *rate* of coin loss at time $$t$$ is
> > proportional to the total supply *at that moment* in time.
>
> This is the key assumption that produces the claimed result.
>
> If you're losing a constant fraction, x (Peter's \lambda), of Bitcoins
> each year, then as soon as the supply increases enough that the constant
> reward, k, corresponds to the constant fraction, ie k = x*N(t), then
> you've hit an equilibrium.  (Likewise if you're losing more than you're
> increasing -- you just need to wait until N(t) decreases enough that you
> reach the same equilibrium point) You don't really need any fancy maths.
>
> But that assumption doesn't need to be true; coins could primarily be
> lost in "black swan" events (due to bugs, wars or disasters) rather
> than at a predictable rate -- with actions taken thereafter such that
> the same event repeating is no longer the same level of catastrophe,
> but instead another new black swan event is required to maintain the same
> loss rate. If that's the case, then the rate at which funds are lost will
> vary chaotically, leading to "inflationary" periods in between events,
> and comparatively strong deflationary shocks when these events occur.
>
> Alternatively, losses could be at a predictable rate that's entirely
> different to the one Peter assumes.
>
> One alternative predictable rate that seems plausible to me is if funds
> are lost due to people not be careful about losing small amounts; even
> though they are careful when amounts are larger. So when 10k BTC was
> worth $40, maybe it doesn't matter if you misplace a hard drive with
> 7500 BTC on it since that's only worth $30; but by the time 7500 BTC
> is worth $150M, maybe you take a bit more care with that, but are still
> not too worried if you lose 1.5mBTC, since that's also only worth $30.
>
> To mathematise that, perhaps there are K people holding Bitcoin, and with
> probability p, each loses $100 (in constant 2009 dollars say, so that we
> can ignore inflation) of that Bitcoin a year through carelessness. For
> an equilibrium to occur in that case, you need:
>
>   N(t) + k - (100/P * Kp) = N(t)
>
> where P is the price of Bitcoin (again in constant 2009 dollars) and k
> is Peter's fixed tail subsidy. Simplifying gives:
>
>   P = K * 100p/k
>
> But k and p are constant by assumption in this scenario, so equilibrium
> is reached only if price (P) is exactly proportional to number of
> users (K). That requires you to have a non-inflationary currency
> (supply is constant) with constant adoption (assume K doesn't change)
> that maintains a constant price (P=K*100p/k) in real terms even if the
> economy is otherwise expanding or contracting.
>
> More importantly, just from a goals point of view, x is something we
> should be finding ways to minimise it over time, not leave constant.
> In fact, you could argue for an even stronger goal: "the real value held
> in BTC lost each year should decrease", that is, x should be decreasing
> faster than 1/(N(t)*P).
>
> Cheers,
> aj
>
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Anthony Towns]

On Sat, Jul 09, 2022 at 08:46:47AM -0400, Peter Todd via bitcoin-dev wrote:
> title:  "Surprisingly, Tail Emission Is Not Inflationary"

> Of course, this isn't realistic as coins are constantly being lost due to
> deaths, forgotten passphrases, boating accidents, etc. These losses are
> independent:

This isn't necessarily true: if the losses are due to a common cause,
then they'll be heavily correlated rather than independent; for example
losses could be caused by a bug in a popular wallet/exchange software
that sends funds to invalid addresses, or by a war or natural disaster
that damages key storage hardware. They're also not independent over
time -- people improve their key storage habits over time; eg switching
to less buggy wallets/exchanges, validating addresses before using them,
using distributed multisig to prevent a localised disaster from being
catastrophic.

> the *rate* of coin loss at time $$t$$ is
> proportional to the total supply *at that moment* in time.

This is the key assumption that produces the claimed result.

If you're losing a constant fraction, x (Peter's \lambda), of Bitcoins
each year, then as soon as the supply increases enough that the constant
reward, k, corresponds to the constant fraction, ie k = x*N(t), then
you've hit an equilibrium.  (Likewise if you're losing more than you're
increasing -- you just need to wait until N(t) decreases enough that you
reach the same equilibrium point) You don't really need any fancy maths.

But that assumption doesn't need to be true; coins could primarily be
lost in "black swan" events (due to bugs, wars or disasters) rather
than at a predictable rate -- with actions taken thereafter such that
the same event repeating is no longer the same level of catastrophe,
but instead another new black swan event is required to maintain the same
loss rate. If that's the case, then the rate at which funds are lost will
vary chaotically, leading to "inflationary" periods in between events,
and comparatively strong deflationary shocks when these events occur.

Alternatively, losses could be at a predictable rate that's entirely
different to the one Peter assumes.

One alternative predictable rate that seems plausible to me is if funds
are lost due to people not be careful about losing small amounts; even
though they are careful when amounts are larger. So when 10k BTC was
worth $40, maybe it doesn't matter if you misplace a hard drive with
7500 BTC on it since that's only worth $30; but by the time 7500 BTC
is worth $150M, maybe you take a bit more care with that, but are still
not too worried if you lose 1.5mBTC, since that's also only worth $30.

To mathematise that, perhaps there are K people holding Bitcoin, and with
probability p, each loses $100 (in constant 2009 dollars say, so that we
can ignore inflation) of that Bitcoin a year through carelessness. For
an equilibrium to occur in that case, you need:

  N(t) + k - (100/P * Kp) = N(t)

where P is the price of Bitcoin (again in constant 2009 dollars) and k
is Peter's fixed tail subsidy. Simplifying gives:

  P = K * 100p/k

But k and p are constant by assumption in this scenario, so equilibrium
is reached only if price (P) is exactly proportional to number of
users (K). That requires you to have a non-inflationary currency
(supply is constant) with constant adoption (assume K doesn't change)
that maintains a constant price (P=K*100p/k) in real terms even if the
economy is otherwise expanding or contracting.

More importantly, just from a goals point of view, x is something we
should be finding ways to minimise it over time, not leave constant.
In fact, you could argue for an even stronger goal: "the real value held
in BTC lost each year should decrease", that is, x should be decreasing
faster than 1/(N(t)*P).

Cheers,
aj

Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[vjudeu]

> We want mining to be is a boring, predictable, business that anyone can do, with as little reward as possible to larger scale miners.

To reach that, miners should earn their block rewards inside Lightning Network. Then, if you want to send some transaction, and you have one satoshi fee, you can produce a Bitcoin block on your CPU, and get a discount on your fee for doing that. Imagine mining a block with difficulty one, and getting some millisatoshis, or even microsatoshis as a reward. Then, to bootstrap that system, it could at first accept any blocks, so existing miners could redirect their shares to such network, then a pool will be able to claim those rewards. And then, when miners will see that the system works as intended, they could switch to solo mining, to get their rewards directly to their addresses.

On 2022-07-10 19:27:28 user Peter Todd via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org> wrote:
> On Sat, Jul 09, 2022 at 09:59:06PM +0000, ZmnSCPxj wrote:
> Good morning e, and list,
> 
> > Yet you posted several links which made that specific correlation, to which I was responding.
> >
> > Math cannot prove how much coin is “lost”, and even if it was provable that the amount of coin lost converges to the amount produced, it is of no consequence - for the reasons I’ve already pointed out. The amount of market production has no impact on market price, just as it does not with any other good.
> >
> > The reason to object to perpetual issuance is the impact on censorship resistance, not on price.
> 
> To clarify about censorship resistance and perpetual issuance ("tail emission"):
> 
> * Suppose I have two blockchains, one with a constant block subsidy, and one which *had* a block subsidy but the block subsidy has become negligible or zero.
> * Now consider a censoring miner.
>   * If the miner rejects particular transactions (i.e. "censors") the miner loses out on the fees of those transactions.
>   * Presumably, the miner does this because it gains other benefits from the censorship, economically equal or better to the earnings lost.
>   * If the blockchain had a block subsidy, then the loss the miner incurs is small relative to the total earnings of each block.
>   * If the blockchain had 0 block subsidy, then the loss the miner incurs is large relative to the total earnings of each block.
>   * Thus, in the latter situation, the external benefit the miner gains from the censorship has to be proportionately larger than in the first situation.

Now let's look at an actual, real-world, attempt to censor Bitcoin via mining:

https://petertodd.org/2016/mit-chainanchor-bribing-miners-to-regulate-bitcoin

The Chain Anchor model was to simply straight up bribe and coerce miners into
only accepting compliant transactions. That's only effective when a large % of
miners actually do that - if a small % do the effect on confirmation time is
miniscule. Obviously, censoring transactions is a significant threat to the
value of Bitcoin - and thus all your Bitcoin-only hashing equipment.

So how do you make a Chain Anchor attack cheaper? By reducing total mining
reward, and making it tied to transaction volume rather than the value of
Bitcoin as a whole.

> Basically, the block subsidy is a market distortion: the block subsidy erodes the value of held coins to pay for the security of coins being moved.

The block subsidy directly ties miner revenue to the total value of Bitcoin:
that's exactly how you want to incentivise a service that keeps Bitcoin secure.

> But the block subsidy is still issued whether or not coins being moved are censored or not censored.
> Thus, there is no incentive, considering *only* the block subsidy, to not censor coin movements.
> Only per-transaction fees have an incentive to not censor coin movements.

The strongest incentive not to censor is because it'll keep Bitcoin valuable.
Not some piddling transaction fees.

> Thus, we should instead prepare for a future where the block subsidy *must* be removed, possibly before the existing schedule removes it, in case a majority coalition of miner ever decides to censor particular transactions without community consensus.
> Fortunately forcing the block subsidy to 0 is a softfork and thus easier to deploy.

Absolutely not.

The historical reality of transaction fees is they've had huge swings, about
10x more volatile than total miner revenue. In the past three years they've
ranged from $8.4 million USD/30-day-average to as little as $140k/30-day-avg,
with the current amount being $370k/30-day-avg. That's a 60x difference.

Meanwhile miner revenue has ranged from $60 million/30-day-avg to $9
million/30-day-avg, a 7x difference.

https://www.blockchain.com/charts/fees-usd-per-transaction

We want mining to be is a boring, predictable, business that anyone can do,
with as little reward as possible to larger scale miners. That's what you need
for maximal decentralization. Making mining a sophisticated business reduces
the pool of entities that can profitably compete in it, and increases their
visibility to government regulation.

Additionally, we want mining to be predictable to avoid having large gluts of
unprofitable mining equipment laying around: mining equipment that could be
used to attack Bitcoin. Fee revenue is obviously doing a much worse job of
achieving that goal than subsidy revenue.


If transaction-fee-only mining was such a good idea, why hasn't any other coin
done it?

-- 
https://petertodd.org 'peter'[:-1]@petertodd.org
_______________________________________________
bitcoin-dev mailing list
bitcoin-dev@lists.linuxfoundation.org
https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev

Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Eric Voskuil]


> On Jul 10, 2022, at 07:17, alicexbt <alicexbt@protonmail.com> wrote:
> Hi ZmnSCPxj,
> 
> 
>> Thus, we should instead prepare for a future where the block subsidy must be removed, possibly before the existing schedule removes it, in case a majority coalition of miner ever decides to censor particular transactions without community consensus.
>> Fortunately forcing the block subsidy to 0 is a softfork and thus easier to deploy.
> 
> `consensus.nSubsidyHalvingInterval` for mainnet in [chainparams.cpp][1] can be decreased to 195000. This will reduce the number of halvings from 34 to 14 and subsidy will be 0 when it becomes less than 0.01 although not sure if this will be a soft fork.

Soft fork, though a bit aggressive, as it would invalidate all existing blocks above the first new halving height block which claimed more than the reduced reward.

Increasing the value would be a hard fork, as it would validate blocks that would previously have been invalid, as opposed to a soft fork, which invalidates blocks that would previously have been valid.

e

> I doubt there will be consensus for it because all the [projections and predictability][2] about bitcoin(currency) would be affected by this change. Maybe everyone can agree with this change if most of the miners start being 'compliant' like one of the coinjoin implementation.
> 
> [1]: https://github.com/bitcoin/bitcoin/blob/master/src/chainparams.cpp#L66
> [2]: https://en.bitcoin.it/wiki/Controlled_supply
> 
> 
> /dev/fd0
> 
> Sent with Proton Mail secure email.
> 
> ------- Original Message -------
> On Saturday, July 9th, 2022 at 9:59 PM, ZmnSCPxj via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org> wrote:
> 
> 
>> Good morning e, and list,
>> 
>>> Yet you posted several links which made that specific correlation, to which I was responding.
>>> Math cannot prove how much coin is “lost”, and even if it was provable that the amount of coin lost converges to the amount produced, it is of no consequence - for the reasons I’ve already pointed out. The amount of market production has no impact on market price, just as it does not with any other good.
>>> The reason to object to perpetual issuance is the impact on censorship resistance, not on price.
>> 
>> 
>> To clarify about censorship resistance and perpetual issuance ("tail emission"):
>> 
>> * Suppose I have two blockchains, one with a constant block subsidy, and one which had a block subsidy but the block subsidy has become negligible or zero.
>> * Now consider a censoring miner.
>> * If the miner rejects particular transactions (i.e. "censors") the miner loses out on the fees of those transactions.
>> * Presumably, the miner does this because it gains other benefits from the censorship, economically equal or better to the earnings lost.
>> * If the blockchain had a block subsidy, then the loss the miner incurs is small relative to the total earnings of each block.
>> * If the blockchain had 0 block subsidy, then the loss the miner incurs is large relative to the total earnings of each block.
>> * Thus, in the latter situation, the external benefit the miner gains from the censorship has to be proportionately larger than in the first situation.
>> 
>> Basically, the block subsidy is a market distortion: the block subsidy erodes the value of held coins to pay for the security of coins being moved.
>> But the block subsidy is still issued whether or not coins being moved are censored or not censored.
>> Thus, there is no incentive, considering only the block subsidy, to not censor coin movements.
>> Only per-transaction fees have an incentive to not censor coin movements.
>> 
>> 
>> Thus, we should instead prepare for a future where the block subsidy must be removed, possibly before the existing schedule removes it, in case a majority coalition of miner ever decides to censor particular transactions without community consensus.
>> Fortunately forcing the block subsidy to 0 is a softfork and thus easier to deploy.
>> 
>> 
>> Regards,
>> ZmnSCPxj
>> _______________________________________________
>> bitcoin-dev mailing list
>> bitcoin-dev@lists.linuxfoundation.org
>> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev

Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Peter Todd]

[-- Attachment #1: Type: text/plain, Size: 1036 bytes --]

On Sun, Jul 10, 2022 at 02:17:36PM +0000, alicexbt via bitcoin-dev wrote:
> Hi ZmnSCPxj,
> 
> 
> > Thus, we should instead prepare for a future where the block subsidy must be removed, possibly before the existing schedule removes it, in case a majority coalition of miner ever decides to censor particular transactions without community consensus.
> > Fortunately forcing the block subsidy to 0 is a softfork and thus easier to deploy.
> 
> `consensus.nSubsidyHalvingInterval` for mainnet in [chainparams.cpp][1] can be decreased to 195000. This will reduce the number of halvings from 34 to 14 and subsidy will be 0 when it becomes less than 0.01 although not sure if this will be a soft fork.

What exactly would the benefit be of going through all the political headache
of a soft fork for what I assume you are thinking would be an insignificant
change in total miner revenue?

Or do you think total transaction fees at that point would be less than
0.01BTC?

-- 
https://petertodd.org 'peter'[:-1]@petertodd.org

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Peter Todd]

[-- Attachment #1: Type: text/plain, Size: 4661 bytes --]

On Sat, Jul 09, 2022 at 09:59:06PM +0000, ZmnSCPxj wrote:
> Good morning e, and list,
> 
> > Yet you posted several links which made that specific correlation, to which I was responding.
> >
> > Math cannot prove how much coin is “lost”, and even if it was provable that the amount of coin lost converges to the amount produced, it is of no consequence - for the reasons I’ve already pointed out. The amount of market production has no impact on market price, just as it does not with any other good.
> >
> > The reason to object to perpetual issuance is the impact on censorship resistance, not on price.
> 
> To clarify about censorship resistance and perpetual issuance ("tail emission"):
> 
> * Suppose I have two blockchains, one with a constant block subsidy, and one which *had* a block subsidy but the block subsidy has become negligible or zero.
> * Now consider a censoring miner.
>   * If the miner rejects particular transactions (i.e. "censors") the miner loses out on the fees of those transactions.
>   * Presumably, the miner does this because it gains other benefits from the censorship, economically equal or better to the earnings lost.
>   * If the blockchain had a block subsidy, then the loss the miner incurs is small relative to the total earnings of each block.
>   * If the blockchain had 0 block subsidy, then the loss the miner incurs is large relative to the total earnings of each block.
>   * Thus, in the latter situation, the external benefit the miner gains from the censorship has to be proportionately larger than in the first situation.

Now let's look at an actual, real-world, attempt to censor Bitcoin via mining:

https://petertodd.org/2016/mit-chainanchor-bribing-miners-to-regulate-bitcoin

The Chain Anchor model was to simply straight up bribe and coerce miners into
only accepting compliant transactions. That's only effective when a large % of
miners actually do that - if a small % do the effect on confirmation time is
miniscule. Obviously, censoring transactions is a significant threat to the
value of Bitcoin - and thus all your Bitcoin-only hashing equipment.

So how do you make a Chain Anchor attack cheaper? By reducing total mining
reward, and making it tied to transaction volume rather than the value of
Bitcoin as a whole.

> Basically, the block subsidy is a market distortion: the block subsidy erodes the value of held coins to pay for the security of coins being moved.

The block subsidy directly ties miner revenue to the total value of Bitcoin:
that's exactly how you want to incentivise a service that keeps Bitcoin secure.

> But the block subsidy is still issued whether or not coins being moved are censored or not censored.
> Thus, there is no incentive, considering *only* the block subsidy, to not censor coin movements.
> Only per-transaction fees have an incentive to not censor coin movements.

The strongest incentive not to censor is because it'll keep Bitcoin valuable.
Not some piddling transaction fees.

> Thus, we should instead prepare for a future where the block subsidy *must* be removed, possibly before the existing schedule removes it, in case a majority coalition of miner ever decides to censor particular transactions without community consensus.
> Fortunately forcing the block subsidy to 0 is a softfork and thus easier to deploy.

Absolutely not.

The historical reality of transaction fees is they've had huge swings, about
10x more volatile than total miner revenue. In the past three years they've
ranged from $8.4 million USD/30-day-average to as little as $140k/30-day-avg,
with the current amount being $370k/30-day-avg. That's a 60x difference.

Meanwhile miner revenue has ranged from $60 million/30-day-avg to $9
million/30-day-avg, a 7x difference.

https://www.blockchain.com/charts/fees-usd-per-transaction

We want mining to be is a boring, predictable, business that anyone can do,
with as little reward as possible to larger scale miners. That's what you need
for maximal decentralization. Making mining a sophisticated business reduces
the pool of entities that can profitably compete in it, and increases their
visibility to government regulation.

Additionally, we want mining to be predictable to avoid having large gluts of
unprofitable mining equipment laying around: mining equipment that could be
used to attack Bitcoin. Fee revenue is obviously doing a much worse job of
achieving that goal than subsidy revenue.


If transaction-fee-only mining was such a good idea, why hasn't any other coin
done it?

-- 
https://petertodd.org 'peter'[:-1]@petertodd.org

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[alicexbt]

Sorry, I made some wrong calculations in the last email. I think the change would just be required in validation.cpp:

https://github.com/bitcoin/bitcoin/blob/a7f3479ba3fda4c9fb29bd7080165744c02ee921/src/validation.cpp#L1472

/dev/fd0

Sent with Proton Mail secure email.

------- Original Message -------
On Sunday, July 10th, 2022 at 2:17 PM, alicexbt via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org> wrote:


> Hi ZmnSCPxj,
>
> > Thus, we should instead prepare for a future where the block subsidy must be removed, possibly before the existing schedule removes it, in case a majority coalition of miner ever decides to censor particular transactions without community consensus.
> > Fortunately forcing the block subsidy to 0 is a softfork and thus easier to deploy.
>
>
> `consensus.nSubsidyHalvingInterval` for mainnet in [chainparams.cpp][1] can be decreased to 195000. This will reduce the number of halvings from 34 to 14 and subsidy will be 0 when it becomes less than 0.01 although not sure if this will be a soft fork.
>
> I doubt there will be consensus for it because all the [projections and predictability][2] about bitcoin(currency) would be affected by this change. Maybe everyone can agree with this change if most of the miners start being 'compliant' like one of the coinjoin implementation.
>
> [1]: https://github.com/bitcoin/bitcoin/blob/master/src/chainparams.cpp#L66
> [2]: https://en.bitcoin.it/wiki/Controlled_supply
>
>
> /dev/fd0
>
> Sent with Proton Mail secure email.
>
>
> ------- Original Message -------
> On Saturday, July 9th, 2022 at 9:59 PM, ZmnSCPxj via bitcoin-dev bitcoin-dev@lists.linuxfoundation.org wrote:
>
>
>
> > Good morning e, and list,
> >
> > > Yet you posted several links which made that specific correlation, to which I was responding.
> > >
> > > Math cannot prove how much coin is “lost”, and even if it was provable that the amount of coin lost converges to the amount produced, it is of no consequence - for the reasons I’ve already pointed out. The amount of market production has no impact on market price, just as it does not with any other good.
> > >
> > > The reason to object to perpetual issuance is the impact on censorship resistance, not on price.
> >
> > To clarify about censorship resistance and perpetual issuance ("tail emission"):
> >
> > * Suppose I have two blockchains, one with a constant block subsidy, and one which had a block subsidy but the block subsidy has become negligible or zero.
> > * Now consider a censoring miner.
> > * If the miner rejects particular transactions (i.e. "censors") the miner loses out on the fees of those transactions.
> > * Presumably, the miner does this because it gains other benefits from the censorship, economically equal or better to the earnings lost.
> > * If the blockchain had a block subsidy, then the loss the miner incurs is small relative to the total earnings of each block.
> > * If the blockchain had 0 block subsidy, then the loss the miner incurs is large relative to the total earnings of each block.
> > * Thus, in the latter situation, the external benefit the miner gains from the censorship has to be proportionately larger than in the first situation.
> >
> > Basically, the block subsidy is a market distortion: the block subsidy erodes the value of held coins to pay for the security of coins being moved.
> > But the block subsidy is still issued whether or not coins being moved are censored or not censored.
> > Thus, there is no incentive, considering only the block subsidy, to not censor coin movements.
> > Only per-transaction fees have an incentive to not censor coin movements.
> >
> > Thus, we should instead prepare for a future where the block subsidy must be removed, possibly before the existing schedule removes it, in case a majority coalition of miner ever decides to censor particular transactions without community consensus.
> > Fortunately forcing the block subsidy to 0 is a softfork and thus easier to deploy.
> >
> > Regards,
> > ZmnSCPxj
> > _______________________________________________
> > bitcoin-dev mailing list
> > bitcoin-dev@lists.linuxfoundation.org
> > https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev

Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[alicexbt]

Hi ZmnSCPxj,


> Thus, we should instead prepare for a future where the block subsidy must be removed, possibly before the existing schedule removes it, in case a majority coalition of miner ever decides to censor particular transactions without community consensus.
> Fortunately forcing the block subsidy to 0 is a softfork and thus easier to deploy.

`consensus.nSubsidyHalvingInterval` for mainnet in [chainparams.cpp][1] can be decreased to 195000. This will reduce the number of halvings from 34 to 14 and subsidy will be 0 when it becomes less than 0.01 although not sure if this will be a soft fork.

I doubt there will be consensus for it because all the [projections and predictability][2] about bitcoin(currency) would be affected by this change. Maybe everyone can agree with this change if most of the miners start being 'compliant' like one of the coinjoin implementation.

[1]: https://github.com/bitcoin/bitcoin/blob/master/src/chainparams.cpp#L66
[2]: https://en.bitcoin.it/wiki/Controlled_supply


/dev/fd0

Sent with Proton Mail secure email.

------- Original Message -------
On Saturday, July 9th, 2022 at 9:59 PM, ZmnSCPxj via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org> wrote:


> Good morning e, and list,
>
> > Yet you posted several links which made that specific correlation, to which I was responding.
> >
> > Math cannot prove how much coin is “lost”, and even if it was provable that the amount of coin lost converges to the amount produced, it is of no consequence - for the reasons I’ve already pointed out. The amount of market production has no impact on market price, just as it does not with any other good.
> >
> > The reason to object to perpetual issuance is the impact on censorship resistance, not on price.
>
>
> To clarify about censorship resistance and perpetual issuance ("tail emission"):
>
> * Suppose I have two blockchains, one with a constant block subsidy, and one which had a block subsidy but the block subsidy has become negligible or zero.
> * Now consider a censoring miner.
> * If the miner rejects particular transactions (i.e. "censors") the miner loses out on the fees of those transactions.
> * Presumably, the miner does this because it gains other benefits from the censorship, economically equal or better to the earnings lost.
> * If the blockchain had a block subsidy, then the loss the miner incurs is small relative to the total earnings of each block.
> * If the blockchain had 0 block subsidy, then the loss the miner incurs is large relative to the total earnings of each block.
> * Thus, in the latter situation, the external benefit the miner gains from the censorship has to be proportionately larger than in the first situation.
>
> Basically, the block subsidy is a market distortion: the block subsidy erodes the value of held coins to pay for the security of coins being moved.
> But the block subsidy is still issued whether or not coins being moved are censored or not censored.
> Thus, there is no incentive, considering only the block subsidy, to not censor coin movements.
> Only per-transaction fees have an incentive to not censor coin movements.
>
>
> Thus, we should instead prepare for a future where the block subsidy must be removed, possibly before the existing schedule removes it, in case a majority coalition of miner ever decides to censor particular transactions without community consensus.
> Fortunately forcing the block subsidy to 0 is a softfork and thus easier to deploy.
>
>
> Regards,
> ZmnSCPxj
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev

Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Jacob Eliosoff]

[-- Attachment #1: Type: text/plain, Size: 10452 bytes --]

> Credit where credit is due: after writing the bulk of this article I
found out
> that Monero developer [smooth_xmr](https://www.reddit.com/user/smooth_xmr/
)
> also observed that tail emission results in a stable coin supply
> [a few years ago](
https://www.reddit.com/r/Monero/comments/4z0azk/maam_28_monero_ask_anything_monday/d6sixyi/
).
> There's probably others too: it's a pretty obvious result.

Fwiw, Joe Lubin, April 2014:  "The expected rate of annual loss and
destruction of ETH will balance the rate of issuance.  Under this dynamic,
a quasi-steady state is reached and the amount of extant ETH no longer
grows."
https://blog.ethereum.org/2014/04/10/the-issuance-model-in-ethereum/

As you say, probably an observation various people have made.  (Ethereum
has had some updates to its issuance model since 2014, in particular
EIP-1559 and the block reward reduction coming with PoS.  But they've had a
fixed rather than halving block subsidy since launch so the question of
whether it implied infinite supply often came up.)


On Sat, Jul 9, 2022, 7:47 AM Peter Todd via bitcoin-dev <
bitcoin-dev@lists.linuxfoundation.org> wrote:

> New blog post:
>
> https://petertodd.org/2022/surprisingly-tail-emission-is-not-inflationary
>
> tl;dr: Due to lost coins, a tail emission/fixed reward actually results in
> a
> stable money supply. Not an (monetarily) inflationary supply.
>
> ...and for the purposes of reply/discussion, attached is the article
> itself in
> markdown format:
>
> ---
> layout: post
> title:  "Surprisingly, Tail Emission Is Not Inflationary"
> date:   2022-07-09
> tags:
> - bitcoin
> - monero
> ---
>
> At present, all notable proof-of-work currencies reward miners with both a
> block
> reward, and transaction fees. With most currencies (including Bitcoin)
> phasing
> out block rewards over time. However in no currency have transaction fees
> consistently been more than 5% to 10% of the total mining
> reward[^fee-in-reward], with the exception of Ethereum, from June 2020 to
> Aug 2021.
> To date no proof-of-work currency has ever operated solely on transaction
> fees[^pow-tweet], and academic analysis has found that in this condition
> block
> generation is unstable.[^instability-without-block-reward] To paraphrase
> Andrew
> Poelstra, it's a scary phase change that no other coin has gone
> through.[^apoelstra-quote]
>
> [^pow-tweet]: [I asked on Twitter](
> https://twitter.com/peterktodd/status/1543231264597090304) and no-one
> replied with counter-examples.
>
> [^fee-in-reward]: [Average Fee Percentage in Total Block Reward](
> https://bitinfocharts.com/comparison/fee_to_reward-btc-eth-bch-ltc-doge-xmr-bsv-dash-zec.html#alltime
> )
>
> [^instability-without-block-reward]: [On the Instability of Bitcoin
> Without the Block Reward](
> https://www.cs.princeton.edu/~arvindn/publications/mining_CCS.pdf)
>
> [^apoelstra-quote]: [From a panel at TABConf 2021](
> https://twitter.com/peterktodd/status/1457066946898317316)
>
> Monero has chosen to implement what they call [tail
> emission](
> https://www.getmonero.org/resources/moneropedia/tail-emission.html):
> a fixed reward per block that continues indefinitely. Dogecoin also has a
> fixed
> reward, which they widely - and incorrectly - refer to as an "abundant"
> supply[^dogecoin-abundant].
>
> [^dogecoin-abundant]: Googling "dogecoin abundant" returns dozens of hits.
>
> This article will show that a fixed block reward does **not** lead to an
> abundant supply. In fact, due to the inevitability of lost coins, a fixed
> reward converges to a **stable** monetary supply that is neither
> inflationary
> nor deflationary, with the total supply proportional to rate of tail
> emission
> and probability of coin loss.
>
> Credit where credit is due: after writing the bulk of this article I found
> out
> that Monero developer [smooth_xmr](https://www.reddit.com/user/smooth_xmr/
> )
> also observed that tail emission results in a stable coin supply
> [a few years ago](
> https://www.reddit.com/r/Monero/comments/4z0azk/maam_28_monero_ask_anything_monday/d6sixyi/
> ).
> There's probably others too: it's a pretty obvious result.
>
>
> <div markdown="1" class="post-toc">
> # Contents
> {:.no_toc}
> 0. TOC
> {:toc}
> </div>
>
> ## Modeling the Fixed-Reward Monetary Supply
>
> Since the number of blocks is large, we can model the monetary supply as a
> continuous function $$N(t)$$, where $$t$$ is a given moment in time. If the
> block reward is fixed we can model the reward as a slope $$k$$ added to an
> initial supply $$N_0$$:
>
> $$
> N(t) = N_0 + kt
> $$
>
> Of course, this isn't realistic as coins are constantly being lost due to
> deaths, forgotten passphrases, boating accidents, etc. These losses are
> independent: I'm not any more or less likely to forget my passphrase
> because
> you recently lost your coins in a boating accident — an accident I probably
> don't even know happened. Since the number of individual coins (and their
> owners) is large — as with the number of blocks — we can model this loss as
> though it happens continuously.
>
> Since coins can only be lost once, the *rate* of coin loss at time $$t$$ is
> proportional to the total supply *at that moment* in time. So let's look
> at the
> *first derivative* of our fixed-reward coin supply:
>
> $$
> \frac{dN(t)}{dt} = k
> $$
>
> ...and subtract from it the lost coins, using $$\lambda$$ as our [coin loss
> constant](https://en.wikipedia.org/wiki/Exponential_decay):
>
> $$
> \frac{dN(t)}{dt} = k - \lambda N(t)
> $$
>
> That's a first-order differential equation, which can be easily solved with
> separation of variables to get:
>
> $$
> N(t) = \frac{k}{\lambda} - Ce^{-\lambda t}
> $$
>
> To remove the integration constant $$C$$, let's look at $$t = 0$$, where
> the
> coin supply is $$N_0$$:
>
> $$
> \begin{align}
>     N_0 &= \frac{k}{\lambda} - Ce^{-\lambda 0} = \frac{k}{\lambda} - C \\
>       C &= \frac{k}{\lambda} - N_0
> \end{align}
> $$
>
> Thus:
>
> $$
> \begin{align}
>     N(t) &= \frac{k}{\lambda} - \left(\frac{k}{\lambda} - N_0
> \right)e^{-\lambda t} \\
>          &= \frac{k}{\lambda} + \left(N_0 - \frac{k}{\lambda}
> \right)e^{-\lambda t}
> \end{align}
> $$
>
>
> ## Long Term Coin Supply
>
> It's easy to see that in the long run, the second half of the coin supply
> equation goes to zero because $$\lim_{t \to \infty} e^{-\lambda t} = 0$$:
>
> $$
> \begin{align}
>     \lim_{t \to \infty} N(t) &= \lim_{t \to \infty} \left[
> \frac{k}{\lambda} + \left(N_0 - \frac{k}{\lambda} \right)e^{-\lambda t}
> \right ] = \frac{k}{\lambda} \\
>                    N(\infty) &= \frac{k}{\lambda}
> \end{align}
> $$
>
> An intuitive explanation for this result is that in the long run, the
> initial
> supply $$N_0$$ doesn't matter, because approximately all of those coins
> will
> eventually be lost. Thus in the long run, the coin supply will converge
> towards
> $$\frac{k}{\lambda}$$, the point where coins are created just as fast as
> they
> are lost.
>
>
> ## Short Term Dynamics and Economic Considerations
>
> Of course, the intuitive explanation for why supply converges to
> $$\frac{k}{\lambda}$$, also tells us that supply must converge fairly
> slowly:
> if 1% of something is lost per year, after 100 years 37% of the initial
> supply
> remains. It's not clear what the rate of lost coins actually is in a
> mature,
> valuable, coin. But 1%/year is likely to be a good guess — quite possibly
> less.
>
> In the case of Monero, they've introduced tail emission at a point where it
> represents a 0.9% apparent monetary inflation rate[^p2pool-tail]. Since
> the number of
> previously lost coins, and the current rate of coin loss, is
> unknown[^unknowable] it's not possible to know exactly what the true
> monetary
> inflation rate is right now. But regardless, the rate will only converge
> towards zero going forward.
>
> [^unknowable]: Being a privacy coin with [shielded amounts](
> https://localmonero.co/blocks/richlist), it's not even possible to get an
> estimate of the total amount of XMR in active circulation.
>
> [^p2pool-tail]: P2Pool operates [a page with real-time date figures](
> https://p2pool.io/tail.html).
>
> If an existing coin decides to implement tail emission as a means to fund
> security, choosing an appropriate emission rate is simple: decide on the
> maximum amount of inflation you are willing to have in the worst case, and
> set
> the tail emission accordingly. In reality monetary inflation will be even
> lower
> on day zero due to lost coins, and in the long run, it will converge
> towards
> zero.
>
> The fact is, economic volatility dwarfs the effect of small amounts of
> inflation. Even a 0.5% inflation rate over 50 years only leads to a 22%
> drop.
> Meanwhile at the time of writing, Bitcoin has dropped 36% in the past
> year, and
> gained 993% over the past 5 years. While this discussion is a nice excuse
> to
> use some mildly interesting math, in the end it's totally pedantic.
>
> ## Could Bitcoin Add Tail Emission?
>
> ...and why could Monero?
>
> Adding tail emission to Bitcoin would be a hard fork: a incompatible rule
> change that existing Bitcoin nodes would reject as invalid. While Monero
> was
> able to get sufficiently broad consensus in the community to implement tail
> emission, it's unclear at best if it would ever be possible to achieve
> that for
> the much larger[^btc-vs-xmr-market-cap] Bitcoin. Additionally, Monero has a
> culture of frequent hard forks that simply does not exist in Bitcoin.
>
> [^btc-vs-xmr-market-cap]: [As of writing](
> https://web.archive.org/web/20220708143920/https://www.coingecko.com/),
> the apparent market cap of Bitcoin is $409 billion, almost 200x larger than
> Monero's $2.3 billion.
>
> Ultimately, as long as a substantial fraction of the Bitcoin community
> continue
> to run full nodes, the only way tail emission could ever be added to
> Bitcoin is
> by convincing that same community that it is a good idea.
>
>
> ## Footnotes
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>

[-- Attachment #2: Type: text/html, Size: 13307 bytes --]

Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[John Tromp]

A parallel discussion is taking place at
https://bitcointalk.org/index.php?topic=5405755.0

Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[vjudeu]

> Adding tail emission to Bitcoin would be a hard fork: a incompatible rule change that existing Bitcoin nodes would reject as invalid.

It won't, because we have zero satoshis. That means, it is possible to create any backward-compatible way of storing amounts. And if we will ever implement things like hiding amounts, then using zero would be a good way to maintain this backward compatibility.

> Ultimately, as long as a substantial fraction of the Bitcoin community continue to run full nodes, the only way tail emission could ever be added to Bitcoin is by convincing that same community that it is a good idea.

Not really, because people that run full nodes, just accepted Segwit and Taproot. They had no choice. And in case of zero satoshis, it could be the same: you would see zero if you look at raw bytes, but you will see non-zero values, if you use some upgraded client, that will support amount hiding, or other features.

Segwit: old nodes see no new signatures, new nodes see all signatures
Zero satoshis: old nodes see new zero amounts, new nodes see all amounts

It is that simple.

On 2022-07-09 14:47:14 user Peter Todd via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org> wrote:
> New blog post:

https://petertodd.org/2022/surprisingly-tail-emission-is-not-inflationary

tl;dr: Due to lost coins, a tail emission/fixed reward actually results in a
stable money supply. Not an (monetarily) inflationary supply.

...and for the purposes of reply/discussion, attached is the article itself in
markdown format:

---
layout: post
title:  "Surprisingly, Tail Emission Is Not Inflationary"
date:   2022-07-09
tags:
- bitcoin
- monero
---

At present, all notable proof-of-work currencies reward miners with both a block
reward, and transaction fees. With most currencies (including Bitcoin) phasing
out block rewards over time. However in no currency have transaction fees
consistently been more than 5% to 10% of the total mining
reward[^fee-in-reward], with the exception of Ethereum, from June 2020 to Aug 2021.
To date no proof-of-work currency has ever operated solely on transaction
fees[^pow-tweet], and academic analysis has found that in this condition block
generation is unstable.[^instability-without-block-reward] To paraphrase Andrew
Poelstra, it's a scary phase change that no other coin has gone through.[^apoelstra-quote]

[^pow-tweet]: [I asked on Twitter](https://twitter.com/peterktodd/status/1543231264597090304) and no-one replied with counter-examples.

[^fee-in-reward]: [Average Fee Percentage in Total Block Reward](https://bitinfocharts.com/comparison/fee_to_reward-btc-eth-bch-ltc-doge-xmr-bsv-dash-zec.html#alltime)

[^instability-without-block-reward]: [On the Instability of Bitcoin Without the Block Reward](https://www.cs.princeton.edu/~arvindn/publications/mining_CCS.pdf)

[^apoelstra-quote]: [From a panel at TABConf 2021](https://twitter.com/peterktodd/status/1457066946898317316)

Monero has chosen to implement what they call [tail
emission](https://www.getmonero.org/resources/moneropedia/tail-emission.html):
a fixed reward per block that continues indefinitely. Dogecoin also has a fixed
reward, which they widely - and incorrectly - refer to as an "abundant" supply[^dogecoin-abundant].

[^dogecoin-abundant]: Googling "dogecoin abundant" returns dozens of hits.

This article will show that a fixed block reward does **not** lead to an
abundant supply. In fact, due to the inevitability of lost coins, a fixed
reward converges to a **stable** monetary supply that is neither inflationary
nor deflationary, with the total supply proportional to rate of tail emission
and probability of coin loss.

Credit where credit is due: after writing the bulk of this article I found out
that Monero developer [smooth_xmr](https://www.reddit.com/user/smooth_xmr/)
also observed that tail emission results in a stable coin supply
[a few years ago](https://www.reddit.com/r/Monero/comments/4z0azk/maam_28_monero_ask_anything_monday/d6sixyi/).
There's probably others too: it's a pretty obvious result.


<div markdown="1" class="post-toc">
# Contents
{:.no_toc}
0. TOC
{:toc}
</div>

## Modeling the Fixed-Reward Monetary Supply

Since the number of blocks is large, we can model the monetary supply as a
continuous function $$N(t)$$, where $$t$$ is a given moment in time. If the
block reward is fixed we can model the reward as a slope $$k$$ added to an
initial supply $$N_0$$:

$$
N(t) = N_0 + kt
$$

Of course, this isn't realistic as coins are constantly being lost due to
deaths, forgotten passphrases, boating accidents, etc. These losses are
independent: I'm not any more or less likely to forget my passphrase because
you recently lost your coins in a boating accident — an accident I probably
don't even know happened. Since the number of individual coins (and their
owners) is large — as with the number of blocks — we can model this loss as
though it happens continuously.

Since coins can only be lost once, the *rate* of coin loss at time $$t$$ is
proportional to the total supply *at that moment* in time. So let's look at the
*first derivative* of our fixed-reward coin supply:

$$
\frac{dN(t)}{dt} = k
$$

...and subtract from it the lost coins, using $$\lambda$$ as our [coin loss
constant](https://en.wikipedia.org/wiki/Exponential_decay):

$$
\frac{dN(t)}{dt} = k - \lambda N(t)
$$

That's a first-order differential equation, which can be easily solved with
separation of variables to get:

$$
N(t) = \frac{k}{\lambda} - Ce^{-\lambda t}
$$

To remove the integration constant $$C$$, let's look at $$t = 0$$, where the
coin supply is $$N_0$$:

$$
\begin{align}
    N_0 &= \frac{k}{\lambda} - Ce^{-\lambda 0} = \frac{k}{\lambda} - C \\
      C &= \frac{k}{\lambda} - N_0
\end{align}
$$

Thus:

$$
\begin{align}
    N(t) &= \frac{k}{\lambda} - \left(\frac{k}{\lambda} - N_0 \right)e^{-\lambda t} \\
         &= \frac{k}{\lambda} + \left(N_0 - \frac{k}{\lambda} \right)e^{-\lambda t}
\end{align}
$$


## Long Term Coin Supply

It's easy to see that in the long run, the second half of the coin supply
equation goes to zero because $$\lim_{t \to \infty} e^{-\lambda t} = 0$$:

$$
\begin{align}
    \lim_{t \to \infty} N(t) &= \lim_{t \to \infty} \left[ \frac{k}{\lambda} + \left(N_0 - \frac{k}{\lambda} \right)e^{-\lambda t} \right ] = \frac{k}{\lambda} \\
                   N(\infty) &= \frac{k}{\lambda}
\end{align}
$$

An intuitive explanation for this result is that in the long run, the initial
supply $$N_0$$ doesn't matter, because approximately all of those coins will
eventually be lost. Thus in the long run, the coin supply will converge towards
$$\frac{k}{\lambda}$$, the point where coins are created just as fast as they
are lost.


## Short Term Dynamics and Economic Considerations

Of course, the intuitive explanation for why supply converges to
$$\frac{k}{\lambda}$$, also tells us that supply must converge fairly slowly:
if 1% of something is lost per year, after 100 years 37% of the initial supply
remains. It's not clear what the rate of lost coins actually is in a mature,
valuable, coin. But 1%/year is likely to be a good guess — quite possibly less.

In the case of Monero, they've introduced tail emission at a point where it
represents a 0.9% apparent monetary inflation rate[^p2pool-tail]. Since the number of
previously lost coins, and the current rate of coin loss, is
unknown[^unknowable] it's not possible to know exactly what the true monetary
inflation rate is right now. But regardless, the rate will only converge
towards zero going forward.

[^unknowable]: Being a privacy coin with [shielded amounts](https://localmonero.co/blocks/richlist), it's not even possible to get an estimate of the total amount of XMR in active circulation.

[^p2pool-tail]: P2Pool operates [a page with real-time date figures](https://p2pool.io/tail.html).

If an existing coin decides to implement tail emission as a means to fund
security, choosing an appropriate emission rate is simple: decide on the
maximum amount of inflation you are willing to have in the worst case, and set
the tail emission accordingly. In reality monetary inflation will be even lower
on day zero due to lost coins, and in the long run, it will converge towards
zero.

The fact is, economic volatility dwarfs the effect of small amounts of
inflation. Even a 0.5% inflation rate over 50 years only leads to a 22% drop.
Meanwhile at the time of writing, Bitcoin has dropped 36% in the past year, and
gained 993% over the past 5 years. While this discussion is a nice excuse to
use some mildly interesting math, in the end it's totally pedantic.

## Could Bitcoin Add Tail Emission?

...and why could Monero?

Adding tail emission to Bitcoin would be a hard fork: a incompatible rule
change that existing Bitcoin nodes would reject as invalid. While Monero was
able to get sufficiently broad consensus in the community to implement tail
emission, it's unclear at best if it would ever be possible to achieve that for
the much larger[^btc-vs-xmr-market-cap] Bitcoin. Additionally, Monero has a
culture of frequent hard forks that simply does not exist in Bitcoin.

[^btc-vs-xmr-market-cap]: [As of writing](https://web.archive.org/web/20220708143920/https://www.coingecko.com/), the apparent market cap of Bitcoin is $409 billion, almost 200x larger than Monero's $2.3 billion.

Ultimately, as long as a substantial fraction of the Bitcoin community continue
to run full nodes, the only way tail emission could ever be added to Bitcoin is
by convincing that same community that it is a good idea.


## Footnotes
_______________________________________________
bitcoin-dev mailing list
bitcoin-dev@lists.linuxfoundation.org
https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev

Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[naman naman]

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Hello ,

Thanks for the correction - it however boils down to the same principle :
diluting other holders, possibly excessively, if you miscalculate the coins
"lost".

Which boils down to the same question again : How would you definitively
know that coins are "lost" or simply not accessed for x amount of time?

Regards,
thenoblebot

On Sat, 9 Jul, 2022, 9:48 pm Peter Todd, <pete@petertodd.org> wrote:

> On Sat, Jul 09, 2022 at 09:43:49PM +0400, naman naman wrote:
> > Hi,
> >
> > This approach raises the obvious question : If someone hasn't had access
> to
> > their coins in a long time (yrs, decades, however you want to define it)
> -
> > and they wish to access/move them after such a time - isn't your proposal
> > simply taking away their ability to do so? Some might call it : stealing
> > their coins.
> >
> > How does one conclusively prove that "lost" coins are "lost forever"?
>
> Re-read the article:
> https://petertodd.org/2022/surprisingly-tail-emission-is-not-inflationary
>
> It has nothing to do with re-assigning ownership of coins.
>
> --
> https://petertodd.org 'peter'[:-1]@petertodd.org
>

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Tobin Harding]

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Hi Peter,

Interesting blog post. 

On Sat, Jul 09, 2022 at 11:31:26AM -0400, Peter Todd via bitcoin-dev wrote:
> On Sat, Jul 09, 2022 at 08:24:51AM -0700, Eric Voskuil wrote:
> > To clarify, price inflation is not caused by market production. Attributing the observed lack of inflation (eg fee %) to loss is an assumed relation.
> 
> My article is a mathematical proof that has nothing to do with observations of
> inflation.
> 
> What I did is prove that if there is tail emission/fixed supply, the coin
> supply will converge towards a fixed amount because the coin supply dependant
> rate of coin loss balances out the fixed rate of coin production.
> 
> That proof has nothing to do with market dynamics and would happen in any
> system, economic or not, with similar underlying dynamics.

I'm not a mathematician but I think your models assumption that coin
loss is proportional to number of coins misses something, correct me if
I'm wrong but as value of coins goes up is it not reasonable to expect
coin loss to go down as people are more careful (not to mention
improvements in tooling and education).

Is it really possible to model coin loss as exponential decay
considering such things (I'm not being facetious, that is a real
question, like I said I'm not a mathematician)?

Cheers,
Tobin.

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[ZmnSCPxj]

Good morning e, and list,

> Yet you posted several links which made that specific correlation, to which I was responding.
>
> Math cannot prove how much coin is “lost”, and even if it was provable that the amount of coin lost converges to the amount produced, it is of no consequence - for the reasons I’ve already pointed out. The amount of market production has no impact on market price, just as it does not with any other good.
>
> The reason to object to perpetual issuance is the impact on censorship resistance, not on price.

To clarify about censorship resistance and perpetual issuance ("tail emission"):

* Suppose I have two blockchains, one with a constant block subsidy, and one which *had* a block subsidy but the block subsidy has become negligible or zero.
* Now consider a censoring miner.
  * If the miner rejects particular transactions (i.e. "censors") the miner loses out on the fees of those transactions.
  * Presumably, the miner does this because it gains other benefits from the censorship, economically equal or better to the earnings lost.
  * If the blockchain had a block subsidy, then the loss the miner incurs is small relative to the total earnings of each block.
  * If the blockchain had 0 block subsidy, then the loss the miner incurs is large relative to the total earnings of each block.
  * Thus, in the latter situation, the external benefit the miner gains from the censorship has to be proportionately larger than in the first situation.

Basically, the block subsidy is a market distortion: the block subsidy erodes the value of held coins to pay for the security of coins being moved.
But the block subsidy is still issued whether or not coins being moved are censored or not censored.
Thus, there is no incentive, considering *only* the block subsidy, to not censor coin movements.
Only per-transaction fees have an incentive to not censor coin movements.


Thus, we should instead prepare for a future where the block subsidy *must* be removed, possibly before the existing schedule removes it, in case a majority coalition of miner ever decides to censor particular transactions without community consensus.
Fortunately forcing the block subsidy to 0 is a softfork and thus easier to deploy.


Regards,
ZmnSCPxj

Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Eric Voskuil]

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Yet you posted several links which made that specific correlation, to which I was responding.

Math cannot prove how much coin is “lost”, and even if it was provable that the amount of coin lost converges to the amount produced, it is of no consequence - for the reasons I’ve already pointed out. The amount of market production has no impact on market price, just as it does not with any other good.

The reason to object to perpetual issuance is the impact on censorship resistance, not on price.

e

> On Jul 9, 2022, at 08:31, Peter Todd <pete@petertodd.org> wrote:
> On Sat, Jul 09, 2022 at 08:24:51AM -0700, Eric Voskuil wrote:
>> To clarify, price inflation is not caused by market production. Attributing the observed lack of inflation (eg fee %) to loss is an assumed relation.
> 
> My article is a mathematical proof that has nothing to do with observations of
> inflation.
> 
> What I did is prove that if there is tail emission/fixed supply, the coin
> supply will converge towards a fixed amount because the coin supply dependant
> rate of coin loss balances out the fixed rate of coin production.
> 
> That proof has nothing to do with market dynamics and would happen in any
> system, economic or not, with similar underlying dynamics.
> 
> -- 
> https://petertodd.org 'peter'[:-1]@petertodd.org


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[bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Eric Voskuil]

In Bitcoin we use the term “supply“ as a reference to the number of coins minted. This colloquialism is commonly conflated with the economic concept of supply, and then injected into a supply/demand relation as if it had the same applicability. Economically supply refers to desire to sell, while demand refers to desire to buy.

e

> On Jul 9, 2022, at 08:24, Eric Voskuil <eric@voskuil.org> wrote:
> 
> To clarify, price inflation is not caused by market production. Attributing the observed lack of inflation (eg fee %) to loss is an assumed relation.
> 
> Even if the amount of loss was known (which it is not), there remains an assumption in the correlation of non-lost coins to price. Demand determines price, not the amount of something in existence, hence the folly of S2F (1/monetary-inflation).
> 
> e
> 
>> On Jul 9, 2022, at 08:15, Peter Todd <pete@petertodd.org> wrote:
>> On Sat, Jul 09, 2022 at 07:26:22AM -0700, Eric Voskuil wrote:
>>>> Due to lost coins, a tail emission/fixed reward actually results in a stable money supply. Not an (monetarily) inflationary supply.
>>> This observation is not a proof of lost coins, that is an assumption.
>> To be clear, are you claiming that there is no proof that coins are lost?
>> --
>> https://petertodd.org 'peter'[:-1]@petertodd.org

Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Peter Todd]

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On Sat, Jul 09, 2022 at 09:43:49PM +0400, naman naman wrote:
> Hi,
> 
> This approach raises the obvious question : If someone hasn't had access to
> their coins in a long time (yrs, decades, however you want to define it) -
> and they wish to access/move them after such a time - isn't your proposal
> simply taking away their ability to do so? Some might call it : stealing
> their coins.
> 
> How does one conclusively prove that "lost" coins are "lost forever"?

Re-read the article: https://petertodd.org/2022/surprisingly-tail-emission-is-not-inflationary

It has nothing to do with re-assigning ownership of coins.

-- 
https://petertodd.org 'peter'[:-1]@petertodd.org

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[naman naman]

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Hi,

This approach raises the obvious question : If someone hasn't had access to
their coins in a long time (yrs, decades, however you want to define it) -
and they wish to access/move them after such a time - isn't your proposal
simply taking away their ability to do so? Some might call it : stealing
their coins.

How does one conclusively prove that "lost" coins are "lost forever"?

Regards,
thenoblebot

On Sat, 9 Jul, 2022, 7:31 pm Peter Todd via bitcoin-dev, <
bitcoin-dev@lists.linuxfoundation.org> wrote:

> On Sat, Jul 09, 2022 at 08:24:51AM -0700, Eric Voskuil wrote:
> > To clarify, price inflation is not caused by market production.
> Attributing the observed lack of inflation (eg fee %) to loss is an assumed
> relation.
>
> My article is a mathematical proof that has nothing to do with
> observations of
> inflation.
>
> What I did is prove that if there is tail emission/fixed supply, the coin
> supply will converge towards a fixed amount because the coin supply
> dependant
> rate of coin loss balances out the fixed rate of coin production.
>
> That proof has nothing to do with market dynamics and would happen in any
> system, economic or not, with similar underlying dynamics.
>
> --
> https://petertodd.org 'peter'[:-1]@petertodd.org
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Peter Todd]

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On Sat, Jul 09, 2022 at 08:24:51AM -0700, Eric Voskuil wrote:
> To clarify, price inflation is not caused by market production. Attributing the observed lack of inflation (eg fee %) to loss is an assumed relation.

My article is a mathematical proof that has nothing to do with observations of
inflation.

What I did is prove that if there is tail emission/fixed supply, the coin
supply will converge towards a fixed amount because the coin supply dependant
rate of coin loss balances out the fixed rate of coin production.

That proof has nothing to do with market dynamics and would happen in any
system, economic or not, with similar underlying dynamics.

-- 
https://petertodd.org 'peter'[:-1]@petertodd.org

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Eric Voskuil]

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To clarify, price inflation is not caused by market production. Attributing the observed lack of inflation (eg fee %) to loss is an assumed relation.

Even if the amount of loss was known (which it is not), there remains an assumption in the correlation of non-lost coins to price. Demand determines price, not the amount of something in existence, hence the folly of S2F (1/monetary-inflation).

e

> On Jul 9, 2022, at 08:15, Peter Todd <pete@petertodd.org> wrote:
> 
> On Sat, Jul 09, 2022 at 07:26:22AM -0700, Eric Voskuil wrote:
>>> Due to lost coins, a tail emission/fixed reward actually results in a stable money supply. Not an (monetarily) inflationary supply.
>> 
>> This observation is not a proof of lost coins, that is an assumption.
> 
> To be clear, are you claiming that there is no proof that coins are lost?
> 
> -- 
> https://petertodd.org 'peter'[:-1]@petertodd.org

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Peter Todd]

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On Sat, Jul 09, 2022 at 07:26:22AM -0700, Eric Voskuil wrote:
> > Due to lost coins, a tail emission/fixed reward actually results in a stable money supply. Not an (monetarily) inflationary supply.
> 
> This observation is not a proof of lost coins, that is an assumption.

To be clear, are you claiming that there is no proof that coins are lost?

-- 
https://petertodd.org 'peter'[:-1]@petertodd.org

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Peter Todd]

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On Sat, Jul 09, 2022 at 04:57:57PM +0200, John Tromp via bitcoin-dev wrote:
> > New blog post:
> > https://petertodd.org/2022/surprisingly-tail-emission-is-not-inflationary
> 
> A Tail Emission is best described as disinflationary; the yearly
> supply inflation steadily decreases toward zero.

_Apparently_ inflation. True monetary inflation includes lost coins - both
intentionally and accidentally lost. It's quite possible that even with tail
emission Monero is currently a monetarily deflationary coin, as the lost coin
rate might be higher than the 0.8% apparent tail emission rate.

We just don't know. Doubly so in the case of monero where its privacy features
hide coin activity.

> > If an existing coin decides to implement tail emission as a means to fund security, choosing an appropriate emission rate is simple: decide on the maximum amount of inflation you are willing to have in the worst case, and set the tail emission accordingly.
> 
> Any coin without a premine starts with infinite inflation. Bitcoin in
> its first 4 years had yearly inflation rates of inf, 100%, 50%, and
> 33%. So deciding on a maximum amount of inflation is deciding on a
> premine.

Hence why I specified an *existing* coin.

> While in the long term, a capped supply doesn't meaningfully differ
> from un uncapped supply [1], the 21M limit is central to Bitcoin's
> identity, and removing this limit results in something that can no
> longer be called Bitcoin.

Personally I think basing your identity on a technical point that isn't even
correct is stupid. And I suspect than when push comes to shove, if in ~10 years
or whatever Bitcoin turns out to be unstable without a reward, the market as a
whole will be happy to redefine Bitcoin to remove the 21M limit. Whether or not
it can do that fast enough to avoid Bitcoin dying first is an open question.

-- 
https://petertodd.org 'peter'[:-1]@petertodd.org

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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[John Tromp]

> New blog post:
> https://petertodd.org/2022/surprisingly-tail-emission-is-not-inflationary

A Tail Emission is best described as disinflationary; the yearly
supply inflation steadily decreases toward zero.

> Dogecoin also has a fixed reward

It started out with random rewards up to 1M doge per block, with the
maximum halving every 100K blocks, until the fixed reward of 10K doge
kicked in at height 600K.

> If an existing coin decides to implement tail emission as a means to fund security, choosing an appropriate emission rate is simple: decide on the maximum amount of inflation you are willing to have in the worst case, and set the tail emission accordingly.

Any coin without a premine starts with infinite inflation. Bitcoin in
its first 4 years had yearly inflation rates of inf, 100%, 50%, and
33%. So deciding on a maximum amount of inflation is deciding on a
premine.

While in the long term, a capped supply doesn't meaningfully differ
from un uncapped supply [1], the 21M limit is central to Bitcoin's
identity, and removing this limit results in something that can no
longer be called Bitcoin.

[1] https://john-tromp.medium.com/a-case-for-using-soft-total-supply-1169a188d153

Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Eric Voskuil]

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> Due to lost coins, a tail emission/fixed reward actually results in a stable money supply. Not an (monetarily) inflationary supply.

This observation is not a proof of lost coins, that is an assumption. It is the provable consequence of market, as opposed to monopoly, production.

https://github.com/libbitcoin/libbitcoin-system/wiki/Inflation-Principle

Mises’ unfortunate error in the application of the Cantillon Effect to gold perpetuates this misperception. One could imagine applying this theory to all goods, not just money, and conclude perpetual loss of value in everything produced, as a consequence of production. One might then be tempted to attribute the fact that this is not observable to loss/depreciation/consumption. While it is certainly possible that the amount of gold produced every year is offset by the amount lost, this of course implies that all of it is lost.

“Circulation” does not determine demand, all money is always held by someone. Changing hands only changes who owns the money, not its purchasing power. See Rothbard’s critique of monetary “velocity”.

e

> On Jul 9, 2022, at 05:47, Peter Todd via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org> wrote:
> 
> New blog post:
> 
> https://petertodd.org/2022/surprisingly-tail-emission-is-not-inflationary
> 
> tl;dr: Due to lost coins, a tail emission/fixed reward actually results in a
> stable money supply. Not an (monetarily) inflationary supply.
> 
> ...and for the purposes of reply/discussion, attached is the article itself in
> markdown format:
> 
> ---
> layout: post
> title:  "Surprisingly, Tail Emission Is Not Inflationary"
> date:   2022-07-09
> tags:
> - bitcoin
> - monero
> ---
> 
> At present, all notable proof-of-work currencies reward miners with both a block
> reward, and transaction fees. With most currencies (including Bitcoin) phasing
> out block rewards over time. However in no currency have transaction fees
> consistently been more than 5% to 10% of the total mining
> reward[^fee-in-reward], with the exception of Ethereum, from June 2020 to Aug 2021.
> To date no proof-of-work currency has ever operated solely on transaction
> fees[^pow-tweet], and academic analysis has found that in this condition block
> generation is unstable.[^instability-without-block-reward] To paraphrase Andrew
> Poelstra, it's a scary phase change that no other coin has gone through.[^apoelstra-quote]
> 
> [^pow-tweet]: [I asked on Twitter](https://twitter.com/peterktodd/status/1543231264597090304) and no-one replied with counter-examples.
> 
> [^fee-in-reward]: [Average Fee Percentage in Total Block Reward](https://bitinfocharts.com/comparison/fee_to_reward-btc-eth-bch-ltc-doge-xmr-bsv-dash-zec.html#alltime)
> 
> [^instability-without-block-reward]: [On the Instability of Bitcoin Without the Block Reward](https://www.cs.princeton.edu/~arvindn/publications/mining_CCS.pdf)
> 
> [^apoelstra-quote]: [From a panel at TABConf 2021](https://twitter.com/peterktodd/status/1457066946898317316)
> 
> Monero has chosen to implement what they call [tail
> emission](https://www.getmonero.org/resources/moneropedia/tail-emission.html):
> a fixed reward per block that continues indefinitely. Dogecoin also has a fixed
> reward, which they widely - and incorrectly - refer to as an "abundant" supply[^dogecoin-abundant].
> 
> [^dogecoin-abundant]: Googling "dogecoin abundant" returns dozens of hits.
> 
> This article will show that a fixed block reward does **not** lead to an
> abundant supply. In fact, due to the inevitability of lost coins, a fixed
> reward converges to a **stable** monetary supply that is neither inflationary
> nor deflationary, with the total supply proportional to rate of tail emission
> and probability of coin loss.
> 
> Credit where credit is due: after writing the bulk of this article I found out
> that Monero developer [smooth_xmr](https://www.reddit.com/user/smooth_xmr/)
> also observed that tail emission results in a stable coin supply
> [a few years ago](https://www.reddit.com/r/Monero/comments/4z0azk/maam_28_monero_ask_anything_monday/d6sixyi/).
> There's probably others too: it's a pretty obvious result.
> 
> 
> <div markdown="1" class="post-toc">
> # Contents
> {:.no_toc}
> 0. TOC
> {:toc}
> </div>
> 
> ## Modeling the Fixed-Reward Monetary Supply
> 
> Since the number of blocks is large, we can model the monetary supply as a
> continuous function $$N(t)$$, where $$t$$ is a given moment in time. If the
> block reward is fixed we can model the reward as a slope $$k$$ added to an
> initial supply $$N_0$$:
> 
> $$
> N(t) = N_0 + kt
> $$
> 
> Of course, this isn't realistic as coins are constantly being lost due to
> deaths, forgotten passphrases, boating accidents, etc. These losses are
> independent: I'm not any more or less likely to forget my passphrase because
> you recently lost your coins in a boating accident — an accident I probably
> don't even know happened. Since the number of individual coins (and their
> owners) is large — as with the number of blocks — we can model this loss as
> though it happens continuously.
> 
> Since coins can only be lost once, the *rate* of coin loss at time $$t$$ is
> proportional to the total supply *at that moment* in time. So let's look at the
> *first derivative* of our fixed-reward coin supply:
> 
> $$
> \frac{dN(t)}{dt} = k
> $$
> 
> ...and subtract from it the lost coins, using $$\lambda$$ as our [coin loss
> constant](https://en.wikipedia.org/wiki/Exponential_decay):
> 
> $$
> \frac{dN(t)}{dt} = k - \lambda N(t)
> $$
> 
> That's a first-order differential equation, which can be easily solved with
> separation of variables to get:
> 
> $$
> N(t) = \frac{k}{\lambda} - Ce^{-\lambda t}
> $$
> 
> To remove the integration constant $$C$$, let's look at $$t = 0$$, where the
> coin supply is $$N_0$$:
> 
> $$
> \begin{align}
>    N_0 &= \frac{k}{\lambda} - Ce^{-\lambda 0} = \frac{k}{\lambda} - C \\
>      C &= \frac{k}{\lambda} - N_0
> \end{align}
> $$
> 
> Thus:
> 
> $$
> \begin{align}
>    N(t) &= \frac{k}{\lambda} - \left(\frac{k}{\lambda} - N_0 \right)e^{-\lambda t} \\
>         &= \frac{k}{\lambda} + \left(N_0 - \frac{k}{\lambda} \right)e^{-\lambda t}
> \end{align}
> $$
> 
> 
> ## Long Term Coin Supply
> 
> It's easy to see that in the long run, the second half of the coin supply
> equation goes to zero because $$\lim_{t \to \infty} e^{-\lambda t} = 0$$:
> 
> $$
> \begin{align}
>    \lim_{t \to \infty} N(t) &= \lim_{t \to \infty} \left[ \frac{k}{\lambda} + \left(N_0 - \frac{k}{\lambda} \right)e^{-\lambda t} \right ] = \frac{k}{\lambda} \\
>                   N(\infty) &= \frac{k}{\lambda}
> \end{align}
> $$
> 
> An intuitive explanation for this result is that in the long run, the initial
> supply $$N_0$$ doesn't matter, because approximately all of those coins will
> eventually be lost. Thus in the long run, the coin supply will converge towards
> $$\frac{k}{\lambda}$$, the point where coins are created just as fast as they
> are lost.
> 
> 
> ## Short Term Dynamics and Economic Considerations
> 
> Of course, the intuitive explanation for why supply converges to
> $$\frac{k}{\lambda}$$, also tells us that supply must converge fairly slowly:
> if 1% of something is lost per year, after 100 years 37% of the initial supply
> remains. It's not clear what the rate of lost coins actually is in a mature,
> valuable, coin. But 1%/year is likely to be a good guess — quite possibly less.
> 
> In the case of Monero, they've introduced tail emission at a point where it
> represents a 0.9% apparent monetary inflation rate[^p2pool-tail]. Since the number of
> previously lost coins, and the current rate of coin loss, is
> unknown[^unknowable] it's not possible to know exactly what the true monetary
> inflation rate is right now. But regardless, the rate will only converge
> towards zero going forward.
> 
> [^unknowable]: Being a privacy coin with [shielded amounts](https://localmonero.co/blocks/richlist), it's not even possible to get an estimate of the total amount of XMR in active circulation.
> 
> [^p2pool-tail]: P2Pool operates [a page with real-time date figures](https://p2pool.io/tail.html).
> 
> If an existing coin decides to implement tail emission as a means to fund
> security, choosing an appropriate emission rate is simple: decide on the
> maximum amount of inflation you are willing to have in the worst case, and set
> the tail emission accordingly. In reality monetary inflation will be even lower
> on day zero due to lost coins, and in the long run, it will converge towards
> zero.
> 
> The fact is, economic volatility dwarfs the effect of small amounts of
> inflation. Even a 0.5% inflation rate over 50 years only leads to a 22% drop.
> Meanwhile at the time of writing, Bitcoin has dropped 36% in the past year, and
> gained 993% over the past 5 years. While this discussion is a nice excuse to
> use some mildly interesting math, in the end it's totally pedantic.
> 
> ## Could Bitcoin Add Tail Emission?
> 
> ...and why could Monero?
> 
> Adding tail emission to Bitcoin would be a hard fork: a incompatible rule
> change that existing Bitcoin nodes would reject as invalid. While Monero was
> able to get sufficiently broad consensus in the community to implement tail
> emission, it's unclear at best if it would ever be possible to achieve that for
> the much larger[^btc-vs-xmr-market-cap] Bitcoin. Additionally, Monero has a
> culture of frequent hard forks that simply does not exist in Bitcoin.
> 
> [^btc-vs-xmr-market-cap]: [As of writing](https://web.archive.org/web/20220708143920/https://www.coingecko.com/), the apparent market cap of Bitcoin is $409 billion, almost 200x larger than Monero's $2.3 billion.
> 
> Ultimately, as long as a substantial fraction of the Bitcoin community continue
> to run full nodes, the only way tail emission could ever be added to Bitcoin is
> by convincing that same community that it is a good idea.
> 
> 
> ## Footnotes
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev

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[bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

[Peter Todd]

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New blog post:

https://petertodd.org/2022/surprisingly-tail-emission-is-not-inflationary

tl;dr: Due to lost coins, a tail emission/fixed reward actually results in a
stable money supply. Not an (monetarily) inflationary supply.

...and for the purposes of reply/discussion, attached is the article itself in
markdown format:

---
layout: post
title:  "Surprisingly, Tail Emission Is Not Inflationary"
date:   2022-07-09
tags:
- bitcoin
- monero
---

At present, all notable proof-of-work currencies reward miners with both a block
reward, and transaction fees. With most currencies (including Bitcoin) phasing
out block rewards over time. However in no currency have transaction fees
consistently been more than 5% to 10% of the total mining
reward[^fee-in-reward], with the exception of Ethereum, from June 2020 to Aug 2021.
To date no proof-of-work currency has ever operated solely on transaction
fees[^pow-tweet], and academic analysis has found that in this condition block
generation is unstable.[^instability-without-block-reward] To paraphrase Andrew
Poelstra, it's a scary phase change that no other coin has gone through.[^apoelstra-quote]

[^pow-tweet]: [I asked on Twitter](https://twitter.com/peterktodd/status/1543231264597090304) and no-one replied with counter-examples.

[^fee-in-reward]: [Average Fee Percentage in Total Block Reward](https://bitinfocharts.com/comparison/fee_to_reward-btc-eth-bch-ltc-doge-xmr-bsv-dash-zec.html#alltime)

[^instability-without-block-reward]: [On the Instability of Bitcoin Without the Block Reward](https://www.cs.princeton.edu/~arvindn/publications/mining_CCS.pdf)

[^apoelstra-quote]: [From a panel at TABConf 2021](https://twitter.com/peterktodd/status/1457066946898317316)

Monero has chosen to implement what they call [tail
emission](https://www.getmonero.org/resources/moneropedia/tail-emission.html):
a fixed reward per block that continues indefinitely. Dogecoin also has a fixed
reward, which they widely - and incorrectly - refer to as an "abundant" supply[^dogecoin-abundant].

[^dogecoin-abundant]: Googling "dogecoin abundant" returns dozens of hits.

This article will show that a fixed block reward does **not** lead to an
abundant supply. In fact, due to the inevitability of lost coins, a fixed
reward converges to a **stable** monetary supply that is neither inflationary
nor deflationary, with the total supply proportional to rate of tail emission
and probability of coin loss.

Credit where credit is due: after writing the bulk of this article I found out
that Monero developer [smooth_xmr](https://www.reddit.com/user/smooth_xmr/)
also observed that tail emission results in a stable coin supply
[a few years ago](https://www.reddit.com/r/Monero/comments/4z0azk/maam_28_monero_ask_anything_monday/d6sixyi/).
There's probably others too: it's a pretty obvious result.


<div markdown="1" class="post-toc">
# Contents
{:.no_toc}
0. TOC
{:toc}
</div>

## Modeling the Fixed-Reward Monetary Supply

Since the number of blocks is large, we can model the monetary supply as a
continuous function $$N(t)$$, where $$t$$ is a given moment in time. If the
block reward is fixed we can model the reward as a slope $$k$$ added to an
initial supply $$N_0$$:

$$
N(t) = N_0 + kt
$$

Of course, this isn't realistic as coins are constantly being lost due to
deaths, forgotten passphrases, boating accidents, etc. These losses are
independent: I'm not any more or less likely to forget my passphrase because
you recently lost your coins in a boating accident — an accident I probably
don't even know happened. Since the number of individual coins (and their
owners) is large — as with the number of blocks — we can model this loss as
though it happens continuously.

Since coins can only be lost once, the *rate* of coin loss at time $$t$$ is
proportional to the total supply *at that moment* in time. So let's look at the
*first derivative* of our fixed-reward coin supply:

$$
\frac{dN(t)}{dt} = k
$$

...and subtract from it the lost coins, using $$\lambda$$ as our [coin loss
constant](https://en.wikipedia.org/wiki/Exponential_decay):

$$
\frac{dN(t)}{dt} = k - \lambda N(t)
$$

That's a first-order differential equation, which can be easily solved with
separation of variables to get:

$$
N(t) = \frac{k}{\lambda} - Ce^{-\lambda t}
$$

To remove the integration constant $$C$$, let's look at $$t = 0$$, where the
coin supply is $$N_0$$:

$$
\begin{align}
    N_0 &= \frac{k}{\lambda} - Ce^{-\lambda 0} = \frac{k}{\lambda} - C \\
      C &= \frac{k}{\lambda} - N_0
\end{align}
$$

Thus:

$$
\begin{align}
    N(t) &= \frac{k}{\lambda} - \left(\frac{k}{\lambda} - N_0 \right)e^{-\lambda t} \\
         &= \frac{k}{\lambda} + \left(N_0 - \frac{k}{\lambda} \right)e^{-\lambda t}
\end{align}
$$


## Long Term Coin Supply

It's easy to see that in the long run, the second half of the coin supply
equation goes to zero because $$\lim_{t \to \infty} e^{-\lambda t} = 0$$:

$$
\begin{align}
    \lim_{t \to \infty} N(t) &= \lim_{t \to \infty} \left[ \frac{k}{\lambda} + \left(N_0 - \frac{k}{\lambda} \right)e^{-\lambda t} \right ] = \frac{k}{\lambda} \\
                   N(\infty) &= \frac{k}{\lambda}
\end{align}
$$

An intuitive explanation for this result is that in the long run, the initial
supply $$N_0$$ doesn't matter, because approximately all of those coins will
eventually be lost. Thus in the long run, the coin supply will converge towards
$$\frac{k}{\lambda}$$, the point where coins are created just as fast as they
are lost.


## Short Term Dynamics and Economic Considerations

Of course, the intuitive explanation for why supply converges to
$$\frac{k}{\lambda}$$, also tells us that supply must converge fairly slowly:
if 1% of something is lost per year, after 100 years 37% of the initial supply
remains. It's not clear what the rate of lost coins actually is in a mature,
valuable, coin. But 1%/year is likely to be a good guess — quite possibly less.

In the case of Monero, they've introduced tail emission at a point where it
represents a 0.9% apparent monetary inflation rate[^p2pool-tail]. Since the number of
previously lost coins, and the current rate of coin loss, is
unknown[^unknowable] it's not possible to know exactly what the true monetary
inflation rate is right now. But regardless, the rate will only converge
towards zero going forward.

[^unknowable]: Being a privacy coin with [shielded amounts](https://localmonero.co/blocks/richlist), it's not even possible to get an estimate of the total amount of XMR in active circulation.

[^p2pool-tail]: P2Pool operates [a page with real-time date figures](https://p2pool.io/tail.html).

If an existing coin decides to implement tail emission as a means to fund
security, choosing an appropriate emission rate is simple: decide on the
maximum amount of inflation you are willing to have in the worst case, and set
the tail emission accordingly. In reality monetary inflation will be even lower
on day zero due to lost coins, and in the long run, it will converge towards
zero.

The fact is, economic volatility dwarfs the effect of small amounts of
inflation. Even a 0.5% inflation rate over 50 years only leads to a 22% drop.
Meanwhile at the time of writing, Bitcoin has dropped 36% in the past year, and
gained 993% over the past 5 years. While this discussion is a nice excuse to
use some mildly interesting math, in the end it's totally pedantic.

## Could Bitcoin Add Tail Emission?

...and why could Monero?

Adding tail emission to Bitcoin would be a hard fork: a incompatible rule
change that existing Bitcoin nodes would reject as invalid. While Monero was
able to get sufficiently broad consensus in the community to implement tail
emission, it's unclear at best if it would ever be possible to achieve that for
the much larger[^btc-vs-xmr-market-cap] Bitcoin. Additionally, Monero has a
culture of frequent hard forks that simply does not exist in Bitcoin.

[^btc-vs-xmr-market-cap]: [As of writing](https://web.archive.org/web/20220708143920/https://www.coingecko.com/), the apparent market cap of Bitcoin is $409 billion, almost 200x larger than Monero's $2.3 billion.

Ultimately, as long as a substantial fraction of the Bitcoin community continue
to run full nodes, the only way tail emission could ever be added to Bitcoin is
by convincing that same community that it is a good idea.


## Footnotes

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