Return-Path: Received: from smtp1.osuosl.org (smtp1.osuosl.org [IPv6:2605:bc80:3010::138]) by lists.linuxfoundation.org (Postfix) with ESMTP id 379FCC002D for ; Mon, 11 Jul 2022 06:15:53 +0000 (UTC) Received: from localhost (localhost [127.0.0.1]) by smtp1.osuosl.org (Postfix) with ESMTP id 1261A83096 for ; Mon, 11 Jul 2022 06:15:53 +0000 (UTC) DKIM-Filter: OpenDKIM Filter v2.11.0 smtp1.osuosl.org 1261A83096 X-Virus-Scanned: amavisd-new at osuosl.org X-Spam-Flag: NO X-Spam-Score: 0.5 X-Spam-Level: X-Spam-Status: No, score=0.5 tagged_above=-999 required=5 tests=[BAYES_40=-0.001, FREEMAIL_FORGED_FROMDOMAIN=0.25, FREEMAIL_FROM=0.001, HEADER_FROM_DIFFERENT_DOMAINS=0.249, HTML_MESSAGE=0.001, LOTS_OF_MONEY=0.001, RCVD_IN_DNSWL_NONE=-0.0001, RCVD_IN_MSPIKE_H2=-0.001, SPF_HELO_NONE=0.001, SPF_PASS=-0.001] autolearn=no autolearn_force=no Received: from smtp1.osuosl.org ([127.0.0.1]) by localhost (smtp1.osuosl.org [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id AndJnMZ2_723 for ; Mon, 11 Jul 2022 06:15:51 +0000 (UTC) X-Greylist: whitelisted by SQLgrey-1.8.0 DKIM-Filter: OpenDKIM Filter v2.11.0 smtp1.osuosl.org 7F9A282974 Received: from mail-lf1-f54.google.com (mail-lf1-f54.google.com [209.85.167.54]) by smtp1.osuosl.org (Postfix) with ESMTPS id 7F9A282974 for ; Mon, 11 Jul 2022 06:15:51 +0000 (UTC) Received: by mail-lf1-f54.google.com with SMTP id t25so7029195lfg.7 for ; Sun, 10 Jul 2022 23:15:51 -0700 (PDT) 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:cc; bh=ZJs/WetT0MTxsZUdKK62bFldPKZCvHrf5rB8BweRHKU=; b=50OUXOuz4/Os+mCGES+Q4SBA7/E3y9J2mwZ32Te/ShttZjOAQMDbr3jDpXc/F/6j1n gBVaUSDbairDAEmr8TRCroc/SlJbdnNTY4GjsXR6u3V8M08xxljjikqrYp4QcmLczIM4 olEfUJ2kRI3TYYVF2NYoNd42nfevG3Qmlid5+9otgeLDRU4ovAn9V6UVa2PdHBYjLgzL M0Uf4VX6p1Wd3035saGc0O+yZQPhSQvuEhNza0195/HGJqVEifGga2ij4JFon7DZF3cP 1Wlp6NVy6VLYsk7Re29blfdSzQe8GoFtck0LAvd2GyrLiaiRWHrXCV4B1Or8vQKCFgla 1GSA== X-Gm-Message-State: AJIora9pr75IsSaLJ4+iKpKanD8N+GmNOTL2YRd5e2xUW5xcn0jJNEX5 U8CzvIqESRCQQLKDvyMX+nYl39qBipHRjjdWBek= X-Google-Smtp-Source: AGRyM1vs8w/XI6vfpEFjnlFS2c/P+pGQFGRPYTUkte8C+7CDXV1r/ElHTLaCeVhusbMKBkePUZnOZ1wmPLJWzDLxgO8= X-Received: by 2002:ac2:4d93:0:b0:489:c69d:59c0 with SMTP id g19-20020ac24d93000000b00489c69d59c0mr9199952lfe.329.1657520149247; Sun, 10 Jul 2022 23:15:49 -0700 (PDT) MIME-Version: 1.0 References: <20220711023247.GA21856@erisian.com.au> In-Reply-To: <20220711023247.GA21856@erisian.com.au> From: Stefan Richter Date: Mon, 11 Jul 2022 08:15:40 +0200 Message-ID: To: Anthony Towns , Bitcoin Protocol Discussion Content-Type: multipart/alternative; boundary="000000000000b4399c05e3817b85" X-Mailman-Approved-At: Mon, 11 Jul 2022 09:56:32 +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: Mon, 11 Jul 2022 06:15:53 -0000 --000000000000b4399c05e3817b85 Content-Type: text/plain; charset="UTF-8" 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 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 > --000000000000b4399c05e3817b85 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
I very much agree with AJ here. This is something I remem= ber 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, distributi= on and technology/best practices. I also think that we have observed this e= ffect in practice since then. The bulk of coins that are supposed to be los= t (via onchain analysis) haven't been moved since at least 2010. Of cou= rse, in most cases, we'll never know, but the assumption of constant lo= ss rate seems unreasonable.

Ch= eers=C2=A0
=C2=A0 Stefan=C2=A0

Anthony Towns vi= a 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:=C2=A0 "Surprisingly, Tail Emission Is Not Inflationary&quo= t;

> Of course, this isn't realistic as coins are constantly being lost= due to
> deaths, forgotten passphrases, boating accidents, etc. These losses ar= e
> 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 Bitco= ins
each year, then as soon as the supply increases enough that the constant reward, k, corresponds to the constant fraction, ie k =3D x*N(t), then
you've hit an equilibrium.=C2=A0 (Likewise if you're losing more th= an 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) rath= er
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 wi= ll
vary chaotically, leading to "inflationary" periods in between ev= ents,
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.<= br>
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:

=C2=A0 N(t) + k - (100/P * Kp) =3D N(t)

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

=C2=A0 P =3D 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=3DK*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 he= ld
in BTC lost each year should decrease", that is, x should be decreasin= g
faster than 1/(N(t)*P).

Cheers,
aj

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