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authorAnthony Towns <aj@erisian.com.au>2022-07-11 12:32:47 +1000
committerbitcoindev <bitcoindev@gnusha.org>2022-07-11 02:32:59 +0000
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Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary
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+ Mon, 11 Jul 2022 12:32:47 +1000
+Date: Mon, 11 Jul 2022 12:32:47 +1000
+From: Anthony Towns <aj@erisian.com.au>
+To: Peter Todd <pete@petertodd.org>,
+ Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
+Message-ID: <20220711023247.GA21856@erisian.com.au>
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+Subject: Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary
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+
+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
+
+