[EM] Approval Voting vs Instant Runoff Voting:

[Richard Moore]

LAYTON Craig <Craig.LAYTON at a...> wrote:

                   This question is open to all the strategically minded
posters; Say with the
                   above utilities (100, 25, 20, 0 - assign A,B,C,D
respectively).  One opinion
                   poll shows (and, being an approval election, these
are approval polls so
                   they show the predicted winner), that A will get 36
percent of the vote, B
                   will get 40, C will get 45 and D will get 44.  You
know that there is some
                   error in opinion polls; say that you are reasonably
sure, based on the
                   poll's claims, that there is a 90% chance that the
opinion poll will be
                   within 5% of the actual vote (that is, 90% chance
that A will get between 31
                   and 41%), and that it is more likely to be closer to
the poll than further
                   away (more likely to be 36% than 41%, but we don't
know how much more
                   likely).  How should you vote?

Although I think you are looking for a mathematical solution, and I do
believe one is
possible, I don't think one is needed (though it would be an interesting
derivation).
I would vote A only without the need to refer to any math. The
difference between A
and B is 75 points. That's a huge gap. If I vote AB, and B beats A
narrowly in the
actual election, then as soon as B starts pushing some program that I am
opposed to
(as seems likely given my low opinion of him), I will regret that vote.
Above all
else when it comes to strategy, I should be able to cast a vote that I
won't regret,
and monotonic methods (such as approval) allow me to do that better than

nonmonotonic systems.

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. As soon as the
results are
published the landscape changes. Say that the 40% B support in the poll
consists
of a large number of voters whose preference is BADC. They may have
stated
they will vote for B only, based on the belief that B is a strong
candidate. Now,
seeing that C looks stronger, they might look for some insurance by
adding A to
their approval vote in the actual election, or in the next poll
(assuming A is a close
enough second for them to feel comfortable doing so). This could raise
A's chances
significantly. Of course, it's possible that a continuing series of
polls would
eventually converge to something close to the actual vote. Still, the
possibility of
election-day strategy shifts exists. So, I don't buy the premise that I
can be
"reasonably sure" of how accurately the results can be predicted by the
poll.

So my choice is based foremost on the utility gap. If my utility scores
for the
candidates are spread evenly (e.g., 100-75-50-25), I might consider data
from
the polls secondarily. But I would take those polls with a grain of
salt.

-- Richard Moore