Approval/IRO Small Vote failures

[Mike Ossipoff]

In a 2-candidate election, where one of them must win, no one would
vote for both candidates unless he/she really considered them both
equally good. So Approval, like Plurality, doesn't fail in a 2-candidate
election. 

Approval is pretty good in a 3-candidate election too, if there's
a candidate who's clearly the middle candidate. The MIddle voters
don't really have a reason to vote for an extreme candidate, since
either an extreme candidate has a majority, in which case it doesn't
matter what the Middle voters do--or else neither extreme has a majority,
in which case Middle has preference majorities over both extremes. If
so, then 1 extreme needs Middle more than the other way around, and
Middle voters needn't vote for anyone other than Middle.

The extreme voters can have a dilemma, if, for all they know,
their own candidate might have a majority, but maybe instead the
opposite extreme has a Plurality.

But if an extreme voter chooses to play it safe & vote for Middle
too, at least he doesn't have to vote for Middle against his favorite,
as he'd have to do in order to give full support to Middle in
Plurlality or IRO.

***

I'm not saying Approval is as good as the best rank-balloting methods,
merely that it's better than the worst.

***

Methods do better with fewer candidates. For instance Bucklin
can't fail to elect a middle Condorcet winner in a 3-candidate
election. In Bucklin the extreme voters have _no_ reason to not
vote Middle 2nd. Therefore, knowing that, the Middle voters have
absolutely no reason to include anyone other than Middle in their
rankings. Bucklin can't fail with 3 candidates. As our examples have
shown, it's easy to make IRO fail with 3 candidates.

***

Good methods will still be good even if there are just a few voters.
There are added aesthetic refinements that could be added, for
results that look better in small elections, but those refinements
aren't really needed. For instance, the more complicated Schwartz
set could be used instead of the Smith set. The use of the Smith
set still enables a method to meet all the criteria in a small election
that it would meet in a big one, but the peculiar character of
a small election can create new situations where the Schwartz set
could be somewhat more appealing, in a way peculiar to a small election,
but not compelling.

***

But maybe if we ever do another multi-alternative vote, we should
specify a tie-breaker, in case the main method returns a tie.
But then again, if that happens, we could just take another vote
among the members of the tie, which might be simpler than
agreeing in advance on a tie-breaker.

***

Mike Ossipoff



The real problem in small elections is the need for a tie-breaker,
because every method is subject to ties in small elections. We
got by without tie-breakers in our methods vote, but we could need
them in a future vote.




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