[EM] Call for Ideas on Automatic Approval Cutoff Finding
Forest Simmons
fsimmons at pcc.edu
Fri Sep 12 13:43:03 PDT 2003
Suppose you were given a set of voted CR ballots, perhaps with
supplemental information such as a tentative approval cutoff. What rule
would you use to adjust the approval cutoff by taking into account the
popularity of the various candidates as manifested by the ballots
themselves, as opposed to published opinion polls?
What supplemental information would you solicit from the voters (through
modified CR ballots) if you could have it?
Suppose, for example, that you asked all voters to submit (along with
their cardinal ratings) the probabilities for each of the candidates being
the final winner of the election, along with a number w between zero and
100 percent expressing their confidence in these probabilities.
Suppose that voters had no strategic incentive to exaggerate any of these
numbers. Then weighted averages (using the w's for the weights) of these
probability estimates could be used as a pooled estimate of the
probabilities of the various candidates winning.
These pooled probabilities could be used to estimate the expected
"cardinal payoff" (i.e. expected utility if the CR values are utilities)
on each ballot, and the cutoff could be a weighted average of the pooled
estimate and the individual estimate.
If the individual is 100 percent confident, then the pooled estimate would
count for nothing. If the individual is zero percent confident, then the
pooled estimate counts for everything. If the individual is 50%
confident, then the pooled estimate and his own estimate receive equal
weight.
If the voter wanted to manipulate, he would have to express high
confidence in his estimate or else it wouldn't effect the outcome much.
But if he expresses high confidence, then he has to live with the results,
since his cutoff will be determined accordingly.
To simplify things, instead of estimating all of the candidate
probabilities, just have each voter indicate which candidate is most
likely to win (in his opinion) along with a confidence number w as before.
These results can still be used to find a pooled estimate, and averaging
the pooled estimate with the cardinality of the most likely candidate on
the ballot is still a reasonable way to pick a cutoff.
In fact, this weighted average will be between the expected CR according
to the pooled estimate of probabilities and the CR level judged most
likely by the voter, and closer to the one that the voter has expressed
more confidence in.
That's just one example. Let's see some creativity!
Forest
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