[EM] Majority winner set

[MIKE OSSIPOFF]

>
>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.

Come on, Markus, that's like asking someone which they like, Bush or
Gore. Changing from IRV to Plurality would be a step sideways.

>
>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.

That's odd, because in the versions that I've heard of, Arrow
stipulates rank balloting, not ratings balloting.

>Therefore, to
>your opinion, Arrow is one of the "head-up-the-ass academics"

One thing Arrow is, is a mystery man about whose impossibility theorem
many many legends and rumors and tales have been woven.

If you want to say that Arrow is one of those academics who are
accurately described by my characterization, I'll take your word for
that.

>who
>doesn't use your "universally accepted" theory.

It isn't a theory. And it isn't mine. But you're 1/3 right, because
it's universally accepted by everyone but you and your you-know-whats
that what voters vote is ballots of the type that are called for by
the voting system in use. They don't vote ratings in rank balloting
elections, for instance.

>
>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.

And I'm saying that that isn't relevant to sincerity, which is about
voting a false preference or avoidably declining to vote a sincere
one (as described in my definition).

Look, if I was going to vote for Gore in the election, believing that
I needed him as a lesser-evil, and then I heard that Nader actually
could have a win, and that information induces me to change my vote
from Gore to Nader, do you claim that I'm voting insincerely when I
vote for my favorite because I've found out that I might be able to
help him win?

Maybe, according to you, sincere voting is possible only in a 0-info
election, or by someone who votes according to principle and couldn't
care less about optimizing his outcome.

>You seem to consider it to be an advantage of Approval
>Voting that he can't express both preferences.

Excuse me, Markus; would you post the date of the archived posting
in which I said that?

>I consider it to be a
>disadvantage of Approval Voting that he can't express both preferences.

Yes, according to popular belief, you improve the situation when you
let people express more preferences. You've just re-stated that
very common popular belief. Actually, however, rank balloting only
makes things worse when it forces people to rank someone else over
their favorite. When rank balloting is counted by any but the few
best ways, it creates a strategic mess, and yes: It's not as good
as Approval. Does that answer your question?

>
>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.

Wrong. Vote for all the candidates whose merit is above the average,
and you maximize your utility expectation when there's zero information
about other people's preferences.

Also, many, probably including you, have an exaggerated notion of
how much, on the average, people's expression of preferences will be
shored in Approval. Actually, since typically a voter will vote for
about half of the candidates, it turns out that he'll be expressing
about half of his pairwise preferences. If he voted for exactly half
of the candidates, he'd be voting pairwise preferences between more
than half of the possible pairs of candidates.

>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.

Markus, are you one of those academics that I was referring to? :-)

With zero information about other voters' preferences, he will,
to maximize his utility expectation, vote for all the candidates who
are above the mean, in his judgement.

With probability information about who will be the 2 frontrunners,
he maximizes his utility expectation if he votes for all the
candidates whose "strategic value" is positive. Strategic value is
defined at http://www.barnsdle.demon.co.uk/vote/sing.html
and also in Merrill's book _Making Multicandidate Elections More
Democratic_.

But most people don't use that approach for Plurality & Approval
strategy. What people will do, with Approval, is vote for the candidate
for whom they'd vote in Plurality, and for everyone whom they
like better.

It would be really silly to vote for all the potential winners, or
to deny votes to all the potential winners. Maybe you'd do that,
but others would know better, and vote as described in the previous
paragraph.

Another way of saying it, if it's strongly felt that a certain 2
candidates will be the frontrunners, is that people will vote for
whichever of those 2 they like more than the other, and also for everyone 
whom they like more than that expected frontrunner for whom
they've voted.


>
>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?

Every voter will vote so as to maximize his utility expectation,
based on his ratings of the candidates and on facts or probability
information about frontrunners, or its absence.

But I'll tell you one thing that they won't do: Unlike voters in
IRV, they'll never vote someone over their favorite.

Mike Ossipoff

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