[EM] Majority winner set

[Markus Schulze]

Dear Mike,

you wrote (2 Dec 2000):
> This, along with small party members' tendency to vote for a lesser-
> evil in 1st place, and the parties reluctance to run more than 1
> candidate, should be mentioned whenever someone talks about IRV's
> "track record".

However, I would like to know whether you would consider a change
from Alternative Voting to Plurality in Australia to be a step forward
or a step backward.

You wrote (2 Dec 2000):
> As you suggested, a version of IIAC could be written about sincere
> ratings. In fact, we often hear IIAC spoken of as if it is about
> sincere ratings, and 2 ballotings, one of which has a candidate who
> isn't in the other balloting. When people refer to that "version",
> they never define it. It would obviously be much wordier and more
> complicated than the version that I quote, and which is almost surely
> Arrow's version: Deleting a loser from the ballots and then recounting
> those ballots should never change who wins.

Arrow presumes that every voter always casts his complete opinion of
the candidates on the ballot. He calls this presumption "Unrestricted
Domain Criterion." This criterion says that the election method must
not restrict the opinion that a given voter can cast. Therefore, to
your opinion, Arrow is one of the "head-up-the-ass academics" who
doesn't use your "universally accepted" theory.

You wrote (2 Dec 2000):
> But what are you saying?
> That the person who doesn't vote Gore over Bush because he wants to
> vote Nader over Gore is voting insincerely?. He can't express both
> preferences. As I said, not doing the impossible can't be counted as
> an act, and so it also isn't an insincere act.

Suppose that this given voter would have approved Nader and disapproved
Gore and Bush if he had no information about the voting behaviour of
the other voters. Then I am saying that this voter votes insincerely
when he approves Nader and Gore and disapproves only Bush after he
has got additional information about the voting behaviour of the
other voters. You seem to consider it to be an advantage of Approval
Voting that he can't express both preferences. I consider it to be a
disadvantage of Approval Voting that he can't express both preferences.

The fact that he can't express both preferences means that he can
influence the election result only when he has very exact information
about the voting behaviour of the other voters. When his information
isn't exact enough then he will probably approve all potential winners
resp. disapprove all potential winners so that his vote has no influence
on the election result.

Is this really what you want?
That a person who doesn't have exact information about the voting
behaviour of the other voters should not be able to influence the
result of the elections?

Markus Schulze

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Date: Sun, 03 Dec 2000 00:31:25 +0100
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Dear Mike,

criteria and election methods are defined on the reported
vNM utilities of the voters. In your example, candidate B
is the Condorcet winner of the reported vNM utilities and
the Schulze method chooses candidate B. Therefore your
example doesn't demonstrate a violation of the Condorcet
criterion.

In your example, you presume that candidate C is the
Condorcet winner of the sincere vNM utilities and that as
some voters vote strategically candidate B is the Condorcet
winner of the reported vNM utilities. But in so far as
criteria and election methods are defined on the reported
vNM utilities, it is only relevant how the voters vote but
not why they vote the way they vote.

Markus Schulze