[EM] Sincere rankings in the methods comparison test

[Bart Ingles]

MIKE OSSIPOFF wrote:
> 
> In Approval, everyone should vote strategically. When there's no information
> about other voters' preferences or voting plans, people should vote for the
> above-mean candidates. But if the voter doesn't have ratings, but only a
> ranking of the candidates, then, as I said, s/he should vote for the best
> half of the candidates. That means that, for a group having a particular
> sincere ranking, half will vote for the middle candidate, as I was saying in
> a previous posting.

I don't think I agree with this, although it coincidentally works out in
the three-candidate case.

The main reason is that, while we have no information about the voters'
utilities for each candidate, the voters themselves surely would.  So
rather than the having the voters estimate utility based on rankings, it
should be the experimenter estimating the distribution of voters.  We
could base our estimates on a linear or gaussian distribution (or its
inverse), for example.  If just looking for a middle-of-the road
estimate in the absence of other information, a linear distribution
seems the most reasonable.

Thus in a four-way race, for a block of voters with identical preference
orders, I would assume that 1/3 approve of three candidates, 1/3 approve
two candidates, and the final 1/3 bullet vote. I believe this would give
results identical to Borda.

The other approach would have all voters approving exactly two
candidates, which doesn't seem correct to me.

Bart