[EM] Approval strategy

[MIKE OSSIPOFF]

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Rob LeGrand wrote:

>Strategy A: Approve all candidates I prefer to the current CRAB 
>first-placer; also approve the first-placer if I prefer him to the 
>second-placer.

>strategy A always homes in on the Condorcet winner when one exists and all 
>voters use the same strategy.

Adam replied:

This is really an outstanding insight. A reliable approval strategy that
requires knowledge of the polling information rather than estimations of
probabilities of victory, and requires ordinal rankings of candidates
rather than estimates of candidate utility.

I reply:

Yes, it's something that hadn't occurred to me, that maybe
the elaborateness of 1-balloting Approval's expectation-maximizing
strategy isn't needed in Repeated Approval. Would that also mean
that Approval DSV doesn't need Weber-Hoffman, etc.?

Adam continued:

While this is only assured to work with CRAB balloting and with all voters
using the strategy, this strategy seems near-optimal for a standard
approval election, and it requires none of the hard-to-come-by estimates of
some of the slightly more accurate methods.

I reply:

It's good if one is reasonably sure that X & Y will be the top 2.
But in 1-balloting Approval, one can improve on that by voting
also for candidates who are better than the election expectation
given that it's between X & Y. And, if a lower probability seems
a better estimate, compared to unity, that X & Y will be top 2,
then it might well be better to further extend these estimates,
by additionally estimating the probability that X & Y will be top 2,
and the probability that neither will be among the top 2, and
roughly estimating the comparative winnabilities of the other
candidates, as I described in "From top 2 to Weber". That gives
estimates of the Pij for Weber. So maybe, for 1-balloting Approval,
it's sometimes better to add to that initial estimate of who the top 2 will 
be, if the probability that X & Y will be top 2 seems more likely
to be some particular lower value, than to be unity.

Of course sometimes one feels fairly sure that a certain 2 will be the top 
2, and maybe that's the only obvious fact about the election.

It's great that there are so many Approval strategies. Different
estimates will seem reliable in different elections.


Mike Ossipoff




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