[EM] Re: Is range voting the panacea we need?

[Chris Benham]

"Bayesian regret".

I  may not be completely  on  top of the "technical" definition of 
 "Bayesian regret", but I know what "regret" is,
and  I  have this explanation from  Warren D. Smith  of what he means by 
the term. This is from page 13  of  his
paper  "Candidate Incentives under different voting systems, and the 
self-reinforcing deterioration of  US democracy",
dated 08/27/04.  Paper 76  from this link:

http://math.temple.edu/~wds/homepage/works.html 
<http://math.temple.edu/%7Ewds/homepage/works.html>

"Every voting system will sometimes arguably produce the "wrong" winner. 
The question is how often this happens and
how severely wrong that winner is. That is an experimental question. The 
experiment can be done by generating, inside
a computer, artificial  "candidates" and "voters"  and running millions 
of  simulated  "elections" under different voting
systems. When doing this experiment, we can artificially force each 
"voter" to have known private mental opinions about
the numerical utility  of  each candidate's possible election victory. 
 There are many possible randomized  "utility generators"
that can be used for that purpose.
Once the election is over, we can use these utilities to assess the 
utility deficit (expressed as a sum over all votes) that
society suffered during that election as a result of that voting system 
sometimes electing a candidate with non-maximal
society-wide utility.
That deficit, when averaged over a vast  number of randomized elections 
with some voting method  V, is called the
Bayesian regret of  V."

In his earlier  "Range Voting" paper he writes:

"Definition. The  "Bayesian regret" of  a voting system is the 
(nonnegative) expected difference between the expected
utility (summed over all voters) of the election winner that systems 
produces, versus the maimum-possible (summed)
utility which would have resulted had the best candidate always won."

Responding to my previous post, Florian Legyel wrote (Mon.Jan.3):

>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.
>
I  can see no real  difference  between my  "sincere ratings" of the 
candidates, and Smith's "private mental opinions about
the numerical utility of each candidate's election victory". (That they 
were on different scales doesn't mean anything.)

Florian Legyel wrote:

>I don't believe WD Smith ever asserted that minimizing Bayesian regret
>is more important than majority rule.
>
> 
>  
>
Really? Then what is your interpretation of  this quote from page 12 of 
 his  "Range Voting" paper, dated 11/28/00,
paper 56 from the same link. Referring to the Majority Loser and 
 Condorcet Loser criteria, he writes:

"Suppose 51% of  voters think ML is lowest utility, by a little; 49% 
think he is highest utility, by a lot. This example is
very important because it demonstrates that the ML and CL criteria are 
poor ones - in this example the  Majority  Loser
*should* win, for the overall good  (i.e. summed utility) of society. QED."

Ralph Suter wrote: (Sun.Jan.2):

>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?
>
All  RV advocates are (at least)  *implicitly* saying that minimizing 
"regret" is more important than majority rule,
by advocating a method that fails  May's axiom,  Majority Loser, and 
 Condorcet Loser.

Ralph again:

>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.
>
In my message, I specified  "voters that just want to vote their full 
sincere ranking".  Of  course, some voters would
find it easier to vote in Approval than to rank the candidates.  In the 
case of  RV with many more slots available than
there are candidates, however, it is  1+1=2 logic that voting will be 
more difficult than with an unrestricted ranking
method because it is possible to have a ranking of  all the candidates 
without rating any of them, but not vice versa.

Chris Benham

> 
>


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