[EM] 02/04/02 - Approval is only for Beauty Contests:

[Richard Moore]

Donald Davison wrote:

 > Approval Voting should never be used in any election in which the `winner
 > to be' is important to most of the voters.
 >
 > Approval Voting should be used in any election in which the `winner 
to be'
 > is not important to most of the voters.
 >
 > A beauty contest is a good example of a election that should use Approval
 > Voting.

Knowing as I do that Donald would never spout empty rhetoric on this list,
I'm sure there's a solid theoretical basis for this statement. While Donald
is looking up the theorem that justifies his argument, I'll offer a few
comments on the topic.

In beauty contests, or in judged athletic competitions (e.g. gymnastics,
skating, diving), where (presumably) the voters have no vested interested
in the outcome (other than their reputation as judges), CR and Borda both
can be expected to work well, because the ratings or rankings given by the
judges will be honest. The finer gradations of Borda and especially CR are
important in such contests, so until Donald presents his theorem we should
not accept his second statement, that Approval "should be used in any
election in which the `winner to be' is not important to most of the voters.

For contests where the voters have a real stake in the outcome, however,
you can expect the voters in a Borda system to sometimes rank candidates
insincerely, and you can expect the voters in a CR system to give each
candidate either the lowest or highest rating (equivalent to their vote
under Approval).

In such contests, Approval does have a powerful compromise-seeking tendency
(a tendency that is of little or no value in the case of impartial judges).
Each voter goes into the election with a certain expectation of utility for
the outcome. Each voter will then approve every candidate that has a higher
utility for that voter than that voter's expectation, and disapprove every
other candidate. This is basic Approval strategy. Most people who have been
reading this list for a while are familiar with the zero-information form
of this, wherein each voter votes for the candidates with greater than
average utility for that voter.

What the voter is saying with his/her ballot, then, is "These are the
candidates I would willingly accept, since any of them would be a better
result for me than I would normally expect in the current political climate.
They might not all be my ideal candidate, but I am willing to compromise
by accepting any of them as the winner."

The actual winner will be the candidate who is viewed as an acceptable
compromise by the largest number of voters. In other words, with the
Approval winner, the smallest number of voters will walk away feeling like
losers. So again, until Donald presents his theorem, we should not accept
his first statement, that Approval "should never be used in any election
in which the `winner to be' is important to most of the voters."

    -- Richard