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From: Gavin Andresen <gavinandresen@gmail.com>
To: Gregory Maxwell <gmaxwell@gmail.com>
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Cc: Bitcoin Development <bitcoin-development@lists.sourceforge.net>
Subject: Re: [Bitcoin-development] Proposed alternatives to the 20MB step
	function
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Let me make sure I understand this proposal:

On Fri, May 8, 2015 at 11:36 PM, Gregory Maxwell <gmaxwell@gmail.com> wrote:

> (*) I believe my currently favored formulation of general dynamic control
> idea is that each miner expresses in their coinbase a preferred size
> between some minimum (e.g. 500k) and the miner's effective-maximum;
> the actual block size can be up to the effective maximum even if the
> preference is lower (you're not forced to make a lower block because you
> stated you wished the limit were lower).  There is a computed maximum
> which is the 33-rd percentile of the last 2016 coinbase preferences
> minus computed_max/52 (rounding up to 1) bytes-- or 500k if thats
> larger. The effective maximum is X bytes more, where X on the range
> [0, computed_maximum] e.g. the miner can double the size of their
> block at most. If X > 0, then the miners must also reach a target
> F(x/computed_maximum) times the bits-difficulty; with F(x) = x^2+1  ---
> so the maximum penalty is 2, with a quadratic shape;  for a given mempool
> there will be some value that maximizes expected income.  (obviously all
> implemented with precise fixed point arithmetic).   The percentile is
> intended to give the preferences of the 33% least preferring miners a
> veto on increases (unless a majority chooses to soft-fork them out). The
> minus-comp_max/52 provides an incentive to slowly shrink the maximum
> if its too large-- x/52 would halve the size in one year if miners
> were doing the lowest difficulty mining. The parameters 500k/33rd,
> -computed_max/52 bytes, and f(x)  I have less strong opinions about;
> and would love to hear reasoned arguments for particular parameters.
>

I'm going to try to figure out how much transaction fee a transaction would
have to pay to bribe a miner to include it. Greg, please let me know if
I've misinterpreted the proposed algorithm. And everybody, please let me
know if I'm making a bone-headed mistake in how I'm computing anything:

Lets say miners are expressing a desire for 600,000 byte blocks in their
coinbases.

computed_max = 600,000 - 600,000/52 = 588,462 bytes.
  --> this is about 23 average-size (500-byte) transactions less than
600,000.
effective_max = 1,176,923

Lets say I want to maintain status quo at 600,000 bytes; how much penalty
do I have?
((600,000-588,462)/588,462)^2 + 1 = 1.00038

How much will that cost me?
The network is hashing at 310PetaHash/sec right now.
Takes 600 seconds to find a block, so 186,000PH per block
186,000 * 0.00038 = 70 extra PH

If it takes 186,000 PH to find a block, and a block is worth 25.13 BTC
(reward plus fees), that 70 PH costs:
(25.13 BTC/block / 186,000 PH/block) * 70 PH = 0.00945 BTC
or at $240 / BTC:  $2.27

... so average transaction fee will have to be about ten cents ($2.27
spread across 23 average-sized transactions) for miners to decide to stay
at 600K blocks. If they fill up 588,462 bytes and don't have some
ten-cent-fee transactions left, they should express a desire to create a
588,462-byte-block and mine with no penalty.

Is that too much?  Not enough?  Average transaction fees today are about 3
cents per transaction.
I created a spreadsheet playing with the parameters:

https://docs.google.com/spreadsheets/d/1zYZfb44Uns8ai0KnoQ-LixDwdhqO5iTI3ZRcihQXlgk/edit?usp=sharing

"We" could tweak the constants or function to get a transaction fee we
think is reasonable... but we really shouldn't be deciding whether
transaction fees are too high, too low, or just right, and after thinking
about this for a while I think any algorithm that ties difficulty to block
size is just a complicated way of dictating minimum fees.

As for some other dynamic algorithm: OK with me. How do we get consensus on
what the best algorithm is? I'm ok with any "don't grow too quickly, give
some reasonable-percentage-minority of miners the ability to block further
increases."

Also relevant here:
"The curious task of economics is to demonstrate to men how little they
really know about what they imagine they can design." - Friedrich August
von Hayek

-- 
--
Gavin Andresen

--089e0112c886dd5d470515c0d614
Content-Type: text/html; charset=UTF-8
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr"><div class=3D"gmail_extra">Let me make sure I understand t=
his proposal:</div><div class=3D"gmail_extra"><br></div><div class=3D"gmail=
_extra"><div class=3D"gmail_quote">On Fri, May 8, 2015 at 11:36 PM, Gregory=
 Maxwell <span dir=3D"ltr">&lt;<a href=3D"mailto:gmaxwell@gmail.com" target=
=3D"_blank">gmaxwell@gmail.com</a>&gt;</span> wrote:<br><blockquote class=
=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;border-left-width:1px;bo=
rder-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">=
<div id=3D":1zn" class=3D"" style=3D"overflow:hidden">(*) I believe my curr=
ently favored formulation of general dynamic control<br>
idea is that each miner expresses in their coinbase a preferred size<br>
between some minimum (e.g. 500k) and the miner&#39;s effective-maximum;<br>
the actual block size can be up to the effective maximum even if the<br>
preference is lower (you&#39;re not forced to make a lower block because yo=
u<br>
stated you wished the limit were lower).=C2=A0 There is a computed maximum<=
br>
which is the 33-rd percentile of the last 2016 coinbase preferences<br>
minus computed_max/52 (rounding up to 1) bytes-- or 500k if thats<br>
larger. The effective maximum is X bytes more, where X on the range<br>
[0, computed_maximum] e.g. the miner can double the size of their<br>
block at most. If X &gt; 0, then the miners must also reach a target<br>
F(x/computed_maximum) times the bits-difficulty; with F(x) =3D x^2+1=C2=A0 =
---<br>
so the maximum penalty is 2, with a quadratic shape;=C2=A0 for a given memp=
ool<br>
there will be some value that maximizes expected income.=C2=A0 (obviously a=
ll<br>
implemented with precise fixed point arithmetic).=C2=A0 =C2=A0The percentil=
e is<br>
intended to give the preferences of the 33% least preferring miners a<br>
veto on increases (unless a majority chooses to soft-fork them out). The<br=
>
minus-comp_max/52 provides an incentive to slowly shrink the maximum<br>
if its too large-- x/52 would halve the size in one year if miners<br>
were doing the lowest difficulty mining. The parameters 500k/33rd,<br>
-computed_max/52 bytes, and f(x)=C2=A0 I have less strong opinions about;<b=
r>
and would love to hear reasoned arguments for particular parameters.</div><=
/blockquote></div><br>I&#39;m going to try to figure out how much transacti=
on fee a transaction would have to pay to bribe a miner to include it. Greg=
, please let me know if I&#39;ve misinterpreted the proposed algorithm. And=
 everybody, please let me know if I&#39;m making a bone-headed mistake in h=
ow I&#39;m computing anything:</div><div class=3D"gmail_extra"><br></div><d=
iv class=3D"gmail_extra">Lets say miners are expressing a desire for 600,00=
0 byte blocks in their coinbases.</div><div class=3D"gmail_extra"><br></div=
><div class=3D"gmail_extra">computed_max =3D 600,000 - 600,000/52 =3D 588,4=
62 bytes.</div><div class=3D"gmail_extra">=C2=A0 --&gt; this is about 23 av=
erage-size (500-byte) transactions less than 600,000.</div><div class=3D"gm=
ail_extra">effective_max =3D=C2=A01,176,923</div><div class=3D"gmail_extra"=
><br></div><div class=3D"gmail_extra">Lets say I want to maintain status qu=
o at 600,000 bytes; how much penalty do I have?</div><div class=3D"gmail_ex=
tra">((600,000-588,462)/588,462)^2 + 1 =3D=C2=A01.00038</div><div class=3D"=
gmail_extra"><br></div><div class=3D"gmail_extra">How much will that cost m=
e?</div><div class=3D"gmail_extra">The network is hashing at 310PetaHash/se=
c right now.</div><div class=3D"gmail_extra">Takes 600 seconds to find a bl=
ock, so 186,000PH per block</div><div class=3D"gmail_extra">186,000 * 0.000=
38 =3D 70 extra PH</div><div class=3D"gmail_extra"><br></div><div class=3D"=
gmail_extra">If it takes 186,000 PH to find a block, and a block is worth 2=
5.13 BTC (reward plus fees), that 70 PH costs:</div><div class=3D"gmail_ext=
ra">(25.13 BTC/block / 186,000 PH/block) * 70 PH =3D 0.00945 BTC</div><div =
class=3D"gmail_extra">or at $240 / BTC: =C2=A0$2.27</div><div class=3D"gmai=
l_extra"><br></div><div class=3D"gmail_extra">... so average transaction fe=
e will have to be about ten cents ($2.27 spread across 23 average-sized tra=
nsactions) for miners to decide to stay at 600K blocks. If they fill up 588=
,462 bytes and don&#39;t have some ten-cent-fee transactions left, they sho=
uld express a desire to create a 588,462-byte-block and mine with no penalt=
y.</div><div class=3D"gmail_extra"><br></div><div class=3D"gmail_extra">Is =
that too much?=C2=A0 Not enough?=C2=A0 Average transaction fees today are a=
bout 3 cents per transaction.</div><div class=3D"gmail_extra">I created a s=
preadsheet playing with the parameters:</div><div class=3D"gmail_extra">=C2=
=A0=C2=A0<a href=3D"https://docs.google.com/spreadsheets/d/1zYZfb44Uns8ai0K=
noQ-LixDwdhqO5iTI3ZRcihQXlgk/edit?usp=3Dsharing">https://docs.google.com/sp=
readsheets/d/1zYZfb44Uns8ai0KnoQ-LixDwdhqO5iTI3ZRcihQXlgk/edit?usp=3Dsharin=
g</a></div><div class=3D"gmail_extra"><br></div><div class=3D"gmail_extra">=
&quot;We&quot; could tweak the constants or function to get a transaction f=
ee we think is reasonable... but we really shouldn&#39;t be deciding whethe=
r transaction fees are too high, too low, or just right, and after thinking=
 about this for a while I think any algorithm that ties difficulty to block=
 size is just a complicated way of dictating minimum fees.</div><div class=
=3D"gmail_extra"><br></div><div class=3D"gmail_extra">As for some other dyn=
amic algorithm: OK with me. How do we get consensus on what the best algori=
thm is? I&#39;m ok with any &quot;don&#39;t grow too quickly, give some rea=
sonable-percentage-minority of miners the ability to block further increase=
s.&quot;</div><div class=3D"gmail_extra"><br></div><div class=3D"gmail_extr=
a"><div class=3D"gmail_extra">Also relevant here:</div>&quot;The curious ta=
sk of economics is to demonstrate to men how little they really know about =
what they imagine they can design.&quot; - Friedrich August von Hayek</div>=
<div class=3D"gmail_extra"><br></div><div class=3D"gmail_extra">-- <br><div=
 class=3D"gmail_signature">--<br>Gavin Andresen<br></div>
</div></div>

--089e0112c886dd5d470515c0d614--