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To: Daniele Pinna <daniele.pinna@gmail.com>
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Cc: bitcoin-dev@lists.linuxfoundation.org
Subject: Re: [bitcoin-dev] "A Transaction Fee Market Exists Without a Block
Size Limit"--new research paper suggests
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Hi Daniele,
I don't think there is any contention over the idea that miners that =
control a larger percentage of the hash rate, h / H, have a =
profitability advantage if you hold all the other variables of the =
miner's profit equation constant. I think this is important: it is a =
centralizing factor similar to other economies of scale. =20
However, that is outside the scope of the result that an individual =
miner's profit per block is always maximized at a finite block size Q* =
if Shannon Entropy about each transaction is communicated during the =
block solution announcement. This result is important because it =
explains how a minimum fee density exists and it shows how miners cannot =
create enormous spam blocks for "no cost," for example. =20
Best regards,
Peter
> 2) Whether it's truly possible for a miner's marginal profit per unit =
of hash to decrease with increasing hashrate in some parametric =
regime.This however directly contradicts the assumption that an optimal =
hashrate exists beyond which the revenue per unit of hash v' < v if h' =
> h.=20
> Q.E.D=20
>=20
> This theorem in turn implies the following corollary:
>=20
> COROLLARY: The marginal profit curve is a monotonically increasing of =
miner hashrate.
>=20
> This simple theorem, suggested implicitly by Gmaxwell disproves any =
and all conclusions of my work. Most importantly, centralization =
pressures will always be present.=20
--Apple-Mail=_A626710B-3D53-4A85-A348-EDDCB866C4AA
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html;
charset=us-ascii
<html><head><meta http-equiv=3D"Content-Type" content=3D"text/html =
charset=3Dus-ascii"></head><body style=3D"word-wrap: break-word; =
-webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">Hi =
Daniele,<div><br></div><div>I don't think there is any contention over =
the idea that miners that control a larger percentage of the hash rate, =
<i>h </i>/ <i>H</i>, have a profitability advantage if you hold all the =
other variables of the miner's profit equation constant. I think =
this is important: it is a centralizing factor similar to other =
economies of scale. </div><div><br></div><div>However, that is =
outside the scope of the result that an individual miner's profit per =
block is always maximized at a finite block size Q* if Shannon Entropy =
about each transaction is communicated during the block solution =
announcement. This result is important because it explains how a =
minimum fee density exists and it shows how miners cannot create =
enormous spam blocks for "no cost," for example. =
</div><div><br></div><div>Best =
regards,</div><div>Peter</div><div><br></div><div><br></div><div><div><blo=
ckquote type=3D"cite"><div class=3D"gmail_extra" style=3D"font-family: =
Helvetica; font-size: medium; font-style: normal; font-variant: normal; =
font-weight: normal; letter-spacing: normal; line-height: normal; =
orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: =
none; white-space: normal; widows: 2; word-spacing: 0px; =
-webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; "><span =
style=3D"font-size: 13px; ">2) Whether it's truly possible for a miner's =
marginal profit per unit of hash to decrease with increasing hashrate in =
some parametric regime.</span>This however directly contradicts the =
assumption that an optimal hashrate exists beyond which the revenue per =
unit of hash <i style=3D"font-size: 12.8000001907349px; =
font-weight: bold; ">v' < v<span =
class=3D"Apple-converted-space"> </span></i><span style=3D"font-size:=
12.8000001907349px; ">if</span><i style=3D"font-size: =
12.8000001907349px; font-weight: bold; "> </i><span =
style=3D"font-size: 12.8000001907349px; "> </span><i =
style=3D"font-size: 12.8000001907349px; "><b>h' > =
h. </b></i></div><div class=3D"gmail_extra" style=3D"font-family: =
Helvetica; font-size: medium; font-style: normal; font-variant: normal; =
font-weight: normal; letter-spacing: normal; line-height: normal; =
orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: =
none; white-space: normal; widows: 2; word-spacing: 0px; =
-webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; "><i =
style=3D"font-size: 12.8000001907349px; =
"><b>Q.E.D </b></i></div><div class=3D"gmail_extra" =
style=3D"font-family: Helvetica; font-size: medium; font-style: normal; =
font-variant: normal; font-weight: normal; letter-spacing: normal; =
line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: =
0px; text-transform: none; white-space: normal; widows: 2; word-spacing: =
0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; =
"><i style=3D"font-size: 12.8000001907349px; "><b><br></b></i></div><div =
class=3D"gmail_extra" style=3D"font-family: Helvetica; font-size: =
medium; font-style: normal; font-variant: normal; font-weight: normal; =
letter-spacing: normal; line-height: normal; orphans: 2; text-align: =
-webkit-auto; text-indent: 0px; text-transform: none; white-space: =
normal; widows: 2; word-spacing: 0px; -webkit-text-size-adjust: auto; =
-webkit-text-stroke-width: 0px; "><span style=3D"font-size: =
12.8000001907349px; ">This theorem in turn implies the following =
corollary:</span></div><div class=3D"gmail_extra" style=3D"font-family: =
Helvetica; font-size: medium; font-style: normal; font-variant: normal; =
font-weight: normal; letter-spacing: normal; line-height: normal; =
orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: =
none; white-space: normal; widows: 2; word-spacing: 0px; =
-webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; "><i =
style=3D"font-size: 12.8000001907349px; "><b><br></b></i></div><div =
class=3D"gmail_extra" style=3D"font-family: Helvetica; font-size: =
medium; font-style: normal; font-variant: normal; font-weight: normal; =
letter-spacing: normal; line-height: normal; orphans: 2; text-align: =
-webkit-auto; text-indent: 0px; text-transform: none; white-space: =
normal; widows: 2; word-spacing: 0px; -webkit-text-size-adjust: auto; =
-webkit-text-stroke-width: 0px; "><span style=3D"font-size: =
12.8000001907349px; "><b>COROLLARY: </b></span><span =
style=3D"font-size: 12.8000001907349px; "><b>The marginal profit curve =
is a monotonically increasing of miner hashrate.</b></span></div><div =
class=3D"gmail_extra" style=3D"font-family: Helvetica; font-size: =
medium; font-style: normal; font-variant: normal; font-weight: normal; =
letter-spacing: normal; line-height: normal; orphans: 2; text-align: =
-webkit-auto; text-indent: 0px; text-transform: none; white-space: =
normal; widows: 2; word-spacing: 0px; -webkit-text-size-adjust: auto; =
-webkit-text-stroke-width: 0px; "><span style=3D"font-size: =
12.8000001907349px; "><b><br></b></span></div><div class=3D"gmail_extra" =
style=3D"font-family: Helvetica; font-size: medium; font-style: normal; =
font-variant: normal; font-weight: normal; letter-spacing: normal; =
line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: =
0px; text-transform: none; white-space: normal; widows: 2; word-spacing: =
0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; =
"><span style=3D"font-size: 12.8000001907349px; ">This simple theorem, =
suggested implicitly by Gmaxwell disproves any and all conclusions of my =
work. Most importantly, centralization pressures will always be =
present. </span></div></blockquote></div><br></div></body></html>=
--Apple-Mail=_A626710B-3D53-4A85-A348-EDDCB866C4AA--
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