[EM] Query re. Approval voting, July 25

[Forest Simmons]

Approval strategy is pretty easy in the case of zero information, as well
as in the case of reliable polls, but as you note, it can be more
troublesome in the case of unreliable polls.

Still, even in those cases there is no reason to approve the candidate
that you like the least or to disapprove the candidate that you like the
best.  Approval is unique among the more popular methods in this regard.

That suggests some variations on Approval that keep this feature while
overcoming the rest of the "unreliable polls" challenge:

First Variation:  The voters indicate which candidates they definitely
approve (yes), and which they definitely disapprove (no). They also
designate one of the candidates as proxy to cast their remaining yes/no
votes. These proxy votes are cast after all of the definite yes/no results
have been made public, so that they are made by someone whose judgment the
voter trusts who has access to (what is in effect) a highly reliable poll,

Second Variation:  The voters indicate their definite approvals and
disapprovals as in the first variation above.  The ballots are collected
and the candidates given a provisional score which is the difference in
their numbers of yes and no votes.

Then each ballot is completed according to the following rule:

Let X be the highest scoring candidate which has already been marked with
a definite yes or no on the ballot.  Mark all of the undecided candidates
on the ballot with the opposite of X's mark.

In other words, if X is approved, then disapprove all of the previously
undecided candidates, otherwise approve them all.

The method winner is the candidate with the greatest approval based on the
completed ballots.

This method can be generalized inductively to CR ballots of arbitrary
resolution, but I'll save that for another posting.

Forest




On Fri, 25 Jul 2003, John B. Hodges wrote:

> Greetings.
>
> I'm satisfied that for the task of filling a single seat in a race
> with multiple candidates, Approval voting can perform well, IF the
> voters use good strategy for setting their approval threshold.
>
> Approval voting, in plain English, attempts to find the candidate
> that the greatest number of voters regard as not unacceptable. This
> is a very modest ambition. One criticism of AV is that it can favor
> mediocrity. For example in a four-candidate race, if all voters
> approve their top three, the winner may be someone ranked second or
> third by a great majority. (If they vote for "anybody but Hanson",
> they may get exactly that.) Arguably this is not a disaster- "hey,
> you marked the ballots"- AV never claims to pick the best, only the
> most-widely-acceptable. But it is still a drawback, compared to other
> voting systems that seek, by some definition, to pick the "best"
> candidate.
>
> There are strategies for setting your approval threshold higher, that
> analytically give better results. If you know enough about the
> candidates to judge how well you like them, but nothing else, then
> approve the "best half", the candidates that are "better than the
> average candidate". If pollsters have made it clear that some are
> running well ahead of others, approve whichever of the front-runners
> you like best, plus anyone else that you like better. These
> strategies are not hard.
>
> My question is about the secondary consequences of the second
> strategy, "favorite front-runner plus". If a widely-believed poll,
> reporting that candidate B is a front-runner, leads to many people
> giving approval votes to B, then there is serious incentive to
> falsify polls. Those supporting B would want to have polls saying B
> was running ahead, those opposing B would want polls saying B was
> runnng behind.
>
> More technically, if the outcome of an election by Approval voting
> depends strongly (or entirely) on the strategy the voters adopt re.
> where to put their approval threshold, and they are sophisticated
> enough to try to put it at the "expected value of the election", then
> there is strong incentive for campaigners to try to manipulate the
> voter's expectations.
>
> In that environment, it may become difficult for the voters to know
> which polls are reliable. They can always choose to ignore all the
> polls and fall back on the "best half" strategy. Then the only
> problem they have is forming an informed opinion of the merits of the
> candidates, which is a problem with many voting rules.
>
> So my question is this: how is Approval voting expected to perform in
> a setting of "propaganda overload", with lots of info of all types
> available but much of it false or shaded, and where there is much
> voter distrust of it all?
>
> --
> ----------------------------------------------
> John B. Hodges, jbhodges@    @usit.net
>
> "The secret of the demagogue is to make himself as stupid as
>   his audience so that they believe they are as clever as he."
>     -- Karl Kraus
>
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