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From: Mark Friedenbach <mark@friedenbach.org>
To: Thomas Voegtlin <thomasv@electrum.org>
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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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I'm on my phone today so I'm somewhat constrained in my reply, but the key
takeaway is that the proposal is a mechanism for miners to trade subsidy
for the increased fees of a larger block. Necessarily it only makes sense
to do so when the marginal fee per KB exceeds the subsidy fee per KB. It
correspondingly makes sense to use a smaller block size if fees are less
than subsidy, but note that fees are not uniform and as the block shrinks
the marginal fee rate goes up..

Limits on both the relative and absolute amount a miner can trade subsidy
for block size prevent incentive edge cases as well as prevent a sharp
shock to the current fee-poor economy (by disallowing adjustment below 1MB)=
.

Also the identity transform was used only for didactic purposes. I fully
expect there to be other, more interesting functions to use.
On May 10, 2015 3:03 PM, "Thomas Voegtlin" <thomasv@electrum.org> wrote:

> Le 08/05/2015 22:33, Mark Friedenbach a =C3=A9crit :
>
> >   * For each block, the miner is allowed to select a different difficul=
ty
> > (nBits) within a certain range, e.g. +/- 25% of the expected difficulty=
,
> > and this miner-selected difficulty is used for the proof of work check.
> In
> > addition to adjusting the hashcash target, selecting a different
> difficulty
> > also raises or lowers the maximum block size for that block by a functi=
on
> > of the difference in difficulty. So increasing the difficulty of the
> block
> > by an additional 25% raises the block limit for that block from 100% of
> the
> > current limit to 125%, and lowering the difficulty by 10% would also
> lower
> > the maximum block size for that block from 100% to 90% of the current
> > limit. For simplicity I will assume a linear identity transform as the
> > function, but a quadratic or other function with compounding marginal
> cost
> > may be preferred.
> >
>
> Sorry but I fail to see how a linear identity transform between block
> size and difficulty would work.
>
> The miner's reward for finding a block is the sum of subsidy and fees:
>
>  R =3D S + F
>
> The probability that the miner will find a block over a time interval is
> inversely proportional to the difficulty D:
>
>  P =3D K / D
>
> where K is a constant that depends on the miner's hashrate. The expected
> reward of the miner is:
>
>  E =3D P * R
>
> Consider that the miner chooses a new difficulty:
>
>  D' =3D D(1 + x).
>
> With a linear identity transform between block size and difficulty, the
> miner will be allowed to collect fees from a block of size: S'=3DS(1+x)
>
> In the best case, collected will be proportional to block size:
>
>  F' =3D F(1+x)
>
> Thus we get:
>
>  E' =3D P' * R' =3D K/(D(1+x)) * (S + F(1+x))
>
>  E' =3D E - x/(1+x) * S * K / D
>
> So with this linear identity transform, increasing block size never
> increases the miners gain. As long as the subsidy exists, the best
> strategy for miners is to reduce block size (i.e. to choose x<0).
>
>
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<p dir=3D"ltr">I&#39;m on my phone today so I&#39;m somewhat constrained in=
 my reply, but the key takeaway is that the proposal is a mechanism for min=
ers to trade subsidy for the increased fees of a larger block. Necessarily =
it only makes sense to do so when the marginal fee per KB exceeds the subsi=
dy fee per KB. It correspondingly makes sense to use a smaller block size i=
f fees are less than subsidy, but note that fees are not uniform and as the=
 block shrinks the marginal fee rate goes up..</p>
<p dir=3D"ltr">Limits on both the relative and absolute amount a miner can =
trade subsidy for block size prevent incentive edge cases as well as preven=
t a sharp shock to the current fee-poor economy (by disallowing adjustment =
below 1MB).</p>
<p dir=3D"ltr">Also the identity transform was used only for didactic purpo=
ses. I fully expect there to be other, more interesting functions to use.</=
p>
<div class=3D"gmail_quote">On May 10, 2015 3:03 PM, &quot;Thomas Voegtlin&q=
uot; &lt;<a href=3D"mailto:thomasv@electrum.org">thomasv@electrum.org</a>&g=
t; wrote:<br type=3D"attribution"><blockquote class=3D"gmail_quote" style=
=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Le 08/05=
/2015 22:33, Mark Friedenbach a =C3=A9crit :<br>
<br>
&gt;=C2=A0 =C2=A0* For each block, the miner is allowed to select a differe=
nt difficulty<br>
&gt; (nBits) within a certain range, e.g. +/- 25% of the expected difficult=
y,<br>
&gt; and this miner-selected difficulty is used for the proof of work check=
. In<br>
&gt; addition to adjusting the hashcash target, selecting a different diffi=
culty<br>
&gt; also raises or lowers the maximum block size for that block by a funct=
ion<br>
&gt; of the difference in difficulty. So increasing the difficulty of the b=
lock<br>
&gt; by an additional 25% raises the block limit for that block from 100% o=
f the<br>
&gt; current limit to 125%, and lowering the difficulty by 10% would also l=
ower<br>
&gt; the maximum block size for that block from 100% to 90% of the current<=
br>
&gt; limit. For simplicity I will assume a linear identity transform as the=
<br>
&gt; function, but a quadratic or other function with compounding marginal =
cost<br>
&gt; may be preferred.<br>
&gt;<br>
<br>
Sorry but I fail to see how a linear identity transform between block<br>
size and difficulty would work.<br>
<br>
The miner&#39;s reward for finding a block is the sum of subsidy and fees:<=
br>
<br>
=C2=A0R =3D S + F<br>
<br>
The probability that the miner will find a block over a time interval is<br=
>
inversely proportional to the difficulty D:<br>
<br>
=C2=A0P =3D K / D<br>
<br>
where K is a constant that depends on the miner&#39;s hashrate. The expecte=
d<br>
reward of the miner is:<br>
<br>
=C2=A0E =3D P * R<br>
<br>
Consider that the miner chooses a new difficulty:<br>
<br>
=C2=A0D&#39; =3D D(1 + x).<br>
<br>
With a linear identity transform between block size and difficulty, the<br>
miner will be allowed to collect fees from a block of size: S&#39;=3DS(1+x)=
<br>
<br>
In the best case, collected will be proportional to block size:<br>
<br>
=C2=A0F&#39; =3D F(1+x)<br>
<br>
Thus we get:<br>
<br>
=C2=A0E&#39; =3D P&#39; * R&#39; =3D K/(D(1+x)) * (S + F(1+x))<br>
<br>
=C2=A0E&#39; =3D E - x/(1+x) * S * K / D<br>
<br>
So with this linear identity transform, increasing block size never<br>
increases the miners gain. As long as the subsidy exists, the best<br>
strategy for miners is to reduce block size (i.e. to choose x&lt;0).<br>
<br>
---------------------------------------------------------------------------=
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>
Widest out-of-the-box monitoring support with 50+ applications<br>
Performance metrics, stats and reports that give you Actionable Insights<br=
>
Deep dive visibility with transaction tracing using APM Insight.<br>
<a href=3D"http://ad.doubleclick.net/ddm/clk/290420510;117567292;y" target=
=3D"_blank">http://ad.doubleclick.net/ddm/clk/290420510;117567292;y</a><br>
_______________________________________________<br>
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pment@lists.sourceforge.net</a><br>
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velopment</a><br>
</blockquote></div>

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