Return-Path: Received: from smtp4.osuosl.org (smtp4.osuosl.org [140.211.166.137]) by lists.linuxfoundation.org (Postfix) with ESMTP id BD83AC002D for ; Wed, 13 Jul 2022 18:32:43 +0000 (UTC) Received: from localhost (localhost [127.0.0.1]) by smtp4.osuosl.org (Postfix) with ESMTP id BB810424AD for ; Wed, 13 Jul 2022 18:30:07 +0000 (UTC) DKIM-Filter: OpenDKIM Filter v2.11.0 smtp4.osuosl.org BB810424AD Authentication-Results: smtp4.osuosl.org; dkim=pass (2048-bit key) header.d=gmail.com header.i=@gmail.com header.a=rsa-sha256 header.s=20210112 header.b=hwmihOuD X-Virus-Scanned: amavisd-new at osuosl.org X-Spam-Flag: NO X-Spam-Score: -2.098 X-Spam-Level: X-Spam-Status: No, score=-2.098 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, DKIM_VALID_EF=-0.1, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_NONE=-0.0001, SPF_HELO_NONE=0.001, SPF_PASS=-0.001] autolearn=ham autolearn_force=no Received: from smtp4.osuosl.org ([127.0.0.1]) by localhost (smtp4.osuosl.org [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id HC0YV35ywHcg for ; Wed, 13 Jul 2022 18:30:05 +0000 (UTC) X-Greylist: whitelisted by SQLgrey-1.8.0 DKIM-Filter: OpenDKIM Filter v2.11.0 smtp4.osuosl.org 41D6B423EF Received: from mail-io1-xd36.google.com (mail-io1-xd36.google.com [IPv6:2607:f8b0:4864:20::d36]) by smtp4.osuosl.org (Postfix) with ESMTPS id 41D6B423EF for ; Wed, 13 Jul 2022 18:30:05 +0000 (UTC) Received: by mail-io1-xd36.google.com with SMTP id l24so11653555ion.13 for ; Wed, 13 Jul 2022 11:30:05 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20210112; h=mime-version:references:in-reply-to:from:date:message-id:subject:to; bh=CfukK0v1mj41U4Y6R7b4Jt4+5eHi4eI6wZKxHKGIb9w=; b=hwmihOuDB4o88NzbzZm1XwpozEx4ZM+3FvBkGMXs31uTKEcfLFXKDU2CZOJFGwtQby B1ZejvCppWMAIGS6ey+mzZD/iOqMLWecPUzsFIfCkawsEkbYSZ2N57jYDAbF1v6YnD0E mSLZPzm7720jKgeElp2L6RtJTRPvSAqZd1t5q3OpQzt+Q0l5QY6+n2wMsnVNUa9lcA8u 2xIzfnB1UrcFBz/G+8FyIYdsWmCaPS9OK+26K7MJ2/Kt/ycDKaa03KRy4AiO3LWJP1mE ZtarscKZ8ubJyGIkQ0I+lEdo8pXq9cwXaTDv/I4WAY7IgSxAwdaGTQbqQuIgL46QiZr0 NzVg== X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20210112; h=x-gm-message-state:mime-version:references:in-reply-to:from:date :message-id:subject:to; bh=CfukK0v1mj41U4Y6R7b4Jt4+5eHi4eI6wZKxHKGIb9w=; b=u3WR+LW28kJ3zAsXHSS/XBA32AGlC2IbBCY+1Wy+X3pCdsEkvu6j49Cgc3lcurKM3j HysTsnXS7bMPRqheY7VRTRA052dgAFPLTJk/3li90AnsMFTVE50PaaoegQyUOAKp/tLU 7Wr2/MZdTOkNND85jO45eA0Tl6lBXUb6o2VZpDw3/OH/uSd+T8tX8rvYu5NBCaXKlB16 nHDVWux7YONrjOL/BU5ifvSSxNMpxcf623zm+GkZU7C7pSebM37O04DHmugolZLpWb6w W6PV35q5PWLUKb1LNAdnsag6BihgpqcXgkuQOiS0qp2aWRWo4Oym/impVSVpWshhIjOE bYBg== X-Gm-Message-State: AJIora8x5XC7b96LUrxy2CGG4IRPLUvs3g3idPHHIMtP6Zsg0XK781id 1id8rFymHOnsUHMOld1TGtOn0SQfRbCpH9nFP484rTT5 X-Google-Smtp-Source: AGRyM1voMwkldNw4PohwX2jg/SAaBQt33Hdh7x/xNnig2tLf3Ifcgi6lMFJ3BfgVK6r5tpjC/DDcTm5v9Pyiyecy4O8= X-Received: by 2002:a05:6638:248b:b0:33f:3a1a:e651 with SMTP id x11-20020a056638248b00b0033f3a1ae651mr2680729jat.139.1657737004267; Wed, 13 Jul 2022 11:30:04 -0700 (PDT) MIME-Version: 1.0 References: <20220711235731.GD20899@erisian.com.au> In-Reply-To: <20220711235731.GD20899@erisian.com.au> From: Zac Greenwood Date: Wed, 13 Jul 2022 20:29:53 +0200 Message-ID: To: Anthony Towns , Bitcoin Protocol Discussion Content-Type: multipart/alternative; boundary="000000000000453b4205e3b3f946" X-Mailman-Approved-At: Wed, 13 Jul 2022 19:02:05 +0000 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: Wed, 13 Jul 2022 18:32:43 -0000 --000000000000453b4205e3b3f946 Content-Type: text/plain; charset="UTF-8" > 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 > --000000000000453b4205e3b3f946 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
>=C2=A0your proo= f is incorrect (or, rather, relies=C2=A0on a hi= ghly unrealistic assumption)

=
The assumption that coin are lost ar a constant rate= is not required. Tail emission will asymptotically decrease the rate of in= flation to zero, at which point the increase in coin exactly matches the am= ount 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 th= e amount of coin grows to infinity. However, lost coin ensures that the poi= nt at which the rate of inflation becomes zero will be reached sooner.

If a black swan event destro= ys 90% of all coin, the constant tail emission will instantly begin to infl= ate the supply at a 10x higher percentage. The inflation expressed as a per= centage will also immediately start to decline because each new coin will i= nflate the total supply with a slightly smaller percentage than the previou= s new coin. The rate of inflation will continue to decline until zero, at w= hich point it again matches the coin-loss induced deflation rate.

Another scenario. Suppose that th= e number of coin lost becomes significantly less for instance because bette= r 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 m= atched the rate of deflation due to coin loss.

<= /div>
Even when the rate at which coin are lost will not b= e constant, a tail emission will tend to an equilibrium.

It must be observed that tail emission cau= ses the total *potential* supply to vary greatly depending on the deflation= rate. In a low-deflation scenario, the supply will have to grow much large= r before an equilibrium can be reached than in a scenario with moderate def= lation 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 us= eful 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 amount= s. 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.
<= div dir=3D"auto">

On Tue, 12 Jul 2022 at 01:58, Anthony Towns via b= itcoin-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 e= ntirely
> > 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/i= nput?i=3DdN%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, gi= ven 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<= br> mechanism (since there's no reason to think miners gaining all the coin= s
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/mail= man/listinfo/bitcoin-dev
--000000000000453b4205e3b3f946--