<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
<title></title>
</head>
<body>
"Bayesian regret".<br>
<br>
I may not be completely on top of the "technical" definition of "Bayesian
regret", but I know what "regret" is,<br>
and I have this explanation from Warren D. Smith of what he means by
the term. This is from page 13 of his<br>
paper "Candidate Incentives under different voting systems, and the self-reinforcing
deterioration of US democracy",<br>
dated 08/27/04. Paper 76 from this link:<br>
<br>
<i><a href="http://math.temple.edu/%7Ewds/homepage/works.html">http://math.temple.edu/~wds/homepage/works.html</a></i><br>
<br>
"Every voting system will sometimes arguably produce the "wrong" winner.
The question is how often this happens and<br>
how severely wrong that winner is. That is an experimental question. The
experiment can be done by generating, inside<br>
a computer, artificial "candidates" and "voters" and running millions of
simulated "elections" under different voting<br>
systems. When doing this experiment, we can artificially force each "voter"
to have known private mental opinions about<br>
the numerical utility of each candidate's possible election victory. There
are many possible randomized "utility generators"<br>
that can be used for that purpose.<br>
Once the election is over, we can use these utilities to assess the utility
deficit (expressed as a sum over all votes) that<br>
society suffered during that election as a result of that voting system sometimes
electing a candidate with non-maximal<br>
society-wide utility.<br>
That deficit, when averaged over a vast number of randomized elections with
some voting method V, is called the<br>
Bayesian regret of V."<br>
<br>
In his earlier "Range Voting" paper he writes:<br>
<br>
"Definition. The "Bayesian regret" of a voting system is the (nonnegative)
expected difference between the expected <br>
utility (summed over all voters) of the election winner that systems produces,
versus the maimum-possible (summed)<br>
utility which would have resulted had the best candidate always won."<br>
<br>
Responding to my previous post, Florian Legyel wrote (Mon.Jan.3):<br>
<blockquote type="cite">
<pre>It's better to be more specific about what is being averaged: WD
Smith's simulations assign, for each voter and candidate, the utility
a given candidate has for that voter.
This is not an "emotion"--it is, in Smith's simulation, a real number
between 0 and 1.</pre>
</blockquote>
I can see no real difference between my "sincere ratings" of the candidates,
and Smith's "private mental opinions about <br>
the numerical utility of each candidate's election victory". (That they were
on different scales doesn't mean anything.)<br>
<br>
Florian Legyel wrote:<br>
<blockquote type="cite">
<pre>I don't believe WD Smith ever asserted that minimizing Bayesian regret
is more important than majority rule.
</pre>
</blockquote>
Really? Then what is your interpretation of this quote from page 12 of his
"Range Voting" paper, dated 11/28/00,<br>
paper 56 from the same link. Referring to the Majority Loser and Condorcet
Loser criteria, he writes:<br>
<br>
"Suppose 51% of voters think ML is lowest utility, by a little; 49% think
he is highest utility, by a lot. This example is<br>
very important because it demonstrates that the ML and CL criteria are poor
ones - in this example the Majority Loser<br>
*should* win, for the overall good (i.e. summed utility) of society. QED."<br>
<br>
Ralph Suter wrote: (Sun.Jan.2):<br>
<blockquote type="cite">
<pre>Chris,
Your arguments aren't making much sense to me. You quote one
advocate of range voting regarding "regret" and majority rule
and suggest that all range voting advocates say the same thing.
What evidence do you have that most RV advocates say this, or
even that it is what the one person you quote really means?</pre>
</blockquote>
All RV advocates are (at least) *implicitly* saying that minimizing "regret"
is more important than majority rule,<br>
by advocating a method that fails May's axiom, Majority Loser, and Condorcet
Loser.<br>
<br>
Ralph again:<br>
<blockquote type="cite">
<pre>As for strategy and the supposed agony voters will suffer while
trying to figure out how to vote in Approval Voting or Range
Voting elections, it certainly can't be true that all or even most
voters will agonize about their decisions or have any reason to
do so, or that the sum total of voter agony in an AV or RV
election would be greater than in an election using a method
you prefer more. If you think so, please explain why.</pre>
</blockquote>
In my message, I specified "voters that just want to vote their full sincere
ranking". Of course, some voters would<br>
find it easier to vote in Approval than to rank the candidates. In the case
of RV with many more slots available than<br>
there are candidates, however, it is 1+1=2 logic that voting will be more
difficult than with an unrestricted ranking<br>
method because it is possible to have a ranking of all the candidates without
rating any of them, but not vice versa.<br>
<br>
Chris Benham<br>
<br>
<blockquote type="cite">
<pre> </pre>
</blockquote>
<br>
<br>
<blockquote type="cite">
<pre>
</pre>
</blockquote>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
</body>
</html>