[EM] Criterion: 0-info mean consistency (0IMC)

[Chris Benham]

Jobst,
You wrote:

>Although I don't believe that all voters are utility maximizers, I still
>think that voters who *are* utility maximizers should be encouraged by
>the election method to vote sincerely. Hence I started studying the
>following minimal criterion:
>
>
>Def. 0-INFO MEAN CONSISTENCY (0IMC).
>Under zero information, voting sincerely must maximize expected utility.
>
This sounds like what I've been calling the  "No Zero-Information 
Strategy" criterion.

>But unfortunately, it is easy to fail the criterion. Even our beloved
>winning votes Condorcet with only 3 candidates *fails* it. 
>
I knew that  the defeat-dropper (winning votes) methods fail this even 
with three candidates. But I don't see that as supporting the idea that 
meeting the criterion is difficult.
Isn't it met by  FPP, IRV, Borda and all the varieties of Borda 
Elimination, DSC (assuming the voter has a sincere full ranking) and others?
(Does random-filling count in your book as "insincere"?  What about 
truncating in a method that meets Later-no-Help but fails Later-no-Harm?)

>So the criterion is already known and has been discussed? Could you give
>me a hint what it had been named then? And is it already known that
>margins Condorcet fulfills the criterion?
>
Yes is the answer to your last question. 

http://lists.electorama.com/pipermail/election-methods-electorama.com/2000-April/003903.html
http://lists.electorama.com/pipermail/election-methods-electorama.com/1998-September/002082.html

Back in September 1998, Blake Cretney wrote this (apparently Winning 
Votes was then called  "Votes-Against"):

>In order to argue in favor of marginal Condorcet, I am going to
>suggest a standard that it passes, but Votes-Against fails.
>
>Sincere Expectation Standard
>Given that a voter has no knowledge about how others will vote, a
>sincere vote must be at least as likely as any insincere vote to
>give results that are in some way better in the eyes of the voter.
>
>Or expressed as a more rigid criterion:
>-----
>Sincere Expectation Criterion (SEC)
>Consider a voter with a preference order between the possible
>outcomes of the election.  Let us call his sincere ballot, X.  Now,
>assuming that every possible legal ballot is equally likely for every
>other voter, there must be some justification for the vote X over any
>other way to fill out the ballot, which I will call Y.
>This justification is given by the following comparisons:
>
>The probability of X electing one of the voter's first choices vs.
>the probability of Y electing one of these choices
>
>The probability of X electing one of the voter's first or second
>choices vs. the probability of Y electing one of these.
>
>The probability of X electing one of the voter's first, second or
>third choices vs. the probability of Y electing one of these.
>... And so on through all the voter's choices
>
>X must either do better in one of these comparisons than Y, or equal
>in all.  Otherwise the sincere vote can not be justified.
>

Chris  Benham
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