[EM] Approval Voting vs Instant Runoff Voting:

[Martin Harper]

Richard Moore wrote:

> About polls in approval voting: Most voters when polled will tend to
> exaggerate
> their preferences in a way they would not in the actual election. The
> reason is
> that they would like to bolster support for their favorite and in a
> non-binding
> poll there is no need to include an insurance vote.

In plurality you want to bolster your support your favourite because 
apparently popular candidates get compromise votes and don't get chucked 
out in favour of compromises. In approval, though, the same doesn't 
apply. I can see only one case where one would want to insincerely dump 
your favourite in a poll:

36% of voters rate A as 1, B as 0.99, and C as 0 ("A voters")
35% of voters rate A as 0.01, B as 1, and C as 0 ("B voters")
29% of voters rate A as 0.01, B as 0, and C as 1 ("C voters")

Now, in a perfect information approval election, all three groups will 
bullet vote, and A(the CW) will win. But what if the some of the B 
voters insincerely reply to polls that they are C voters, so the polls 
report %ages of 36%, 32%, 32%, respectively, with error rates of +/-3%. 
Then in the election the A voters will vote AB to make sure of keeping 
out C.

This is a bit of a stretch, though: it requires very specific 
percentages, and precisely 3% of B voters to lie - if more B voters than 
that are insincere, then the optimum strategy for A voters will go back 
to bullet voting, and A will once more win. In addition B is the guy who 
we'd want to elect, on the basis of maximum utility, so the fact that 
imperfect information causes us to elect him/her would seem to be a good 
thing!

I played around with a case where you'd want to insincerely bullet vote 
in a poll, but couldn't find one that worked. Can you provide one?

Martin