From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: from smtp3.osuosl.org (smtp3.osuosl.org [IPv6:2605:bc80:3010::136]) by lists.linuxfoundation.org (Postfix) with ESMTP id 1BF99C002D for ; Mon, 11 Jul 2022 02:32:59 +0000 (UTC) Received: from localhost (localhost [127.0.0.1]) by smtp3.osuosl.org (Postfix) with ESMTP id DBBC760E95 for ; Mon, 11 Jul 2022 02:32:58 +0000 (UTC) DKIM-Filter: OpenDKIM Filter v2.11.0 smtp3.osuosl.org DBBC760E95 X-Virus-Scanned: amavisd-new at osuosl.org X-Spam-Flag: NO X-Spam-Score: 3.299 X-Spam-Level: *** X-Spam-Status: No, score=3.299 tagged_above=-999 required=5 tests=[BAYES_50=0.8, LOTS_OF_MONEY=0.001, MONEY_NOHTML=2.499, SPF_HELO_PASS=-0.001, SPF_PASS=-0.001, UNPARSEABLE_RELAY=0.001] autolearn=no autolearn_force=no Received: from smtp3.osuosl.org ([127.0.0.1]) by localhost (smtp3.osuosl.org [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id Sn-V7rgFCMlY for ; Mon, 11 Jul 2022 02:32:57 +0000 (UTC) X-Greylist: from auto-whitelisted by SQLgrey-1.8.0 DKIM-Filter: OpenDKIM Filter v2.11.0 smtp3.osuosl.org 6E2BD60E94 Received: from azure.erisian.com.au (azure.erisian.com.au [172.104.61.193]) by smtp3.osuosl.org (Postfix) with ESMTPS id 6E2BD60E94 for ; Mon, 11 Jul 2022 02:32:57 +0000 (UTC) Received: from aj@azure.erisian.com.au (helo=sapphire.erisian.com.au) by azure.erisian.com.au with esmtpsa (Exim 4.92 #3 (Debian)) id 1oAjEC-00047c-8l; Mon, 11 Jul 2022 12:32:54 +1000 Received: by sapphire.erisian.com.au (sSMTP sendmail emulation); Mon, 11 Jul 2022 12:32:47 +1000 Date: Mon, 11 Jul 2022 12:32:47 +1000 From: Anthony Towns To: Peter Todd , Bitcoin Protocol Discussion Message-ID: <20220711023247.GA21856@erisian.com.au> References: MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline In-Reply-To: User-Agent: Mutt/1.10.1 (2018-07-13) X-Spam-Score-int: -18 X-Spam-Bar: - Subject: Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary X-BeenThere: bitcoin-dev@lists.linuxfoundation.org X-Mailman-Version: 2.1.15 Precedence: list List-Id: Bitcoin Protocol Discussion List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-List-Received-Date: Mon, 11 Jul 2022 02:32:59 -0000 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