[EM] Markus: MMC. Why WV vs Margins matters.

[Markus Schulze]

Dear Mike,

you wrote (4 March 2003):
> MMC says:
>
>    If there is a set of candidates such that a majority of the voters
>    strictly prefers each candidate of this set to each candidate
>    outside this set, then the winner must be a candidate of this set.
>
> If that were MMC, then no method would meet MMC. Saying that a
> majority prefer the candidates in set S to all the other candidates,
> but not saying anything about how they vote, no one can guarantee who
> will win then.
>
> Either you should speak of a majority _voting_ the candidates in S
> over all the other candidates, or else, when saying only that they
> prefer the candidates in S to all the others, you should add the
> stipulation that they vote sincerely.

We've talked about this before in connection with a paper by Pattanaik
and Peleg ("P&P"). I agree to Blake Cretney's way of seeing this.

Blake wrote to Mike (28 Jan 2002):
> Having said all that, I'll get to how I interpret P&P.  P&P talk about
> ballots, and criteria and methods based on those ballots.  By ballots I
> could just as easily say preference orders.  I don't think P&P intend to
> propose a theory in which the preference orders are mental states, but
> the method works on actual ballots, so the ballots must be "sincere",
> whatever that might mean.  They ignore the sincerity issue.  They just
> have methods and criteria that refer to preference orders.  But where
> those preference orders come from isn't their concern.  For you,
> preference order implies sincere preferences, and you recognize that a
> real-world method can only work on cast votes.  But for P&P, a method is
> just a function from a hypothetical set of preference orders to a set of
> winners.

I absolutely agree with Blake: "A method is just a function from
a hypothetical set of preference orders to a set of winners.
Where the preference orders come from is of no concern."

Markus Schulze

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