[EM] re: CR/Approval and cutoffs

[Kevin Venzke]

Forest,

I'm afraid I'm still not sure.  There has to be some utility boundary, where on
one side the candidate should be approved, and on the other side, disapproved.
Surely a candidate can sit right on this boundary.  Where else might this boundary
be, besides the expected utility?

Another thought: Suppose there is an Approval election with three candidates,
ABC, each with equal perceived odds of winning, with respective utilities (for
you) of 100%, 50%, and 0%.  Your expectation is thus 50%, exactly B's utility.

If you approve A only, you can break a tie between AB or AC.
If you approve A and B, you can break a tie between BC or AC.

AB and BC are equally likely to occur, and the utility gain from breaking either
tie is the same.  So I think there is no good argument for or against approving B.

I can see only approving A if you were actually guaranteed 50% from the election.
But for that to be true, B's odds would have to be 100%.  In that case, either
a) your "A" vote gives A some chance of winning, or b) your vote is just expressive,
because there is (or is thought to be) no potential gain from any way of voting.

> > The bottom line, for me, is that it would not be good to have every voter
> > disapprove the candidates at their expectation level.
> 
> Evidently you are not including the case of zero expectation.

Right.  What I meant was: It would not be best if the rule always followed,
was that expectation-level candidates are never approved.  If that were the
rule, however, I don't think it would really be a disaster unless the number
of slots and candidates were so few that it actually made a difference on a
lot of voters' ballots.


Kevin Venzke
stepjak at yahoo.fr


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