[EM] When will Approval Voting defeat a majority candidate

[MIKE OSSIPOFF]

Approval does much better than IRV in terms of social utility,
the utility of the winner, summed over all the voters, in simulations.

A book, _Making Multicandidate Elections More Democratic_, by
Samuel Merrill describes Merrill's simulations in more detail.
But, by social utility, Approval is clearly better than IRV.

IRV's SU problem is what Merrill refers to as the squeeze problem,
if I remember his term correctly. The SU maximizing candidate is
often eliminated in IRV because of not having as many 1st choice
votes as candidates to the sides, in the issue-space.
And so IRV then jumps to a low SU extreme.

Even if the scenario doesn't start out looking like that, it tends
to get that way, if candidates' 1st choice support tapers gradually
away from the middle SU maximizing candidate. Then, eliminations start
at the extremes, and send transfered votes inward, which pile up
on candidates to the sides of the middle candidate. Of course that
can cause those candidates to eliminate the middle candidate even
if the Middle initially had more votes than anyone. For instance:

[Numbers on the left are numbers of voters. The letters after the
numbers are the order in which those voters rank candidates.

60: ABCDE
70: BACDE
100: C
83: DECBA
75: EDCBA

Not only is C the Condorcet candidate, who'd beat each of the others
in pairwise comparisons, and the voter median candidate (it's been
shown that, with 1 dimensional issue-space, the voter median candidate
is the SU maximizer), but C also is favorite to more voters than
any other candidate is. But when the extremes get eliminated, and
transfer inward, we find that the candidates to the sides of the
voter-median SU maximizer are now big enough to eliminate that
candidate.

And, as you said, Approval beats IRV not only in SU, but also in
not ever giving anyone any incentive to dump their favorite by
voting someone else over him/her. With Approval, everyone would always
feel free to fully vote for their favorite. That can't be said
for Plurality or IRV.

Add IRV's nonmonotonicity, its bizarre ability to act oppositely
to voters' reaction to new information, and one can only wonder
how the CVD IRVies chose to promote IRV.

Mike Ossipoff





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