[EM] 50 percent approval.

Forest Simmons fsimmons at pcc.edu
Sat Apr 19 13:26:02 PDT 2003

Actually, in the zero information case, with utilities chosen at random
there is at least a 50 percent chance that more than half of the
candidates will get at least 50 percent approval.

To see this, consider a random choice of utilities that results in fewer
than half of the candidates getting more than fifty percent approval.

There is an equally likely distribution of utilities in which zero
information strategy would change all of the disapproved candidates into
approved candidates.

This new distribution of utilities is obtained by subtracting all of the
old utilities from 100 (or whatever the max utility is).

That takes care of the zero information case.

We have already treated the two front runner case below: rational strategy
will have every voter approving at least one of them, so one of them will
end up with at least fifty percent approval.

Another interesting case is when polling information is available, but
there are not two definite front runners.

In this case, suppose that Joe Weinstein's max information strategy is
used in which each voter marks the approval cutoff so as to make the
probability of one of the candidates above the mark winning as close to
fifty percent as possible.

If the voters' probability estimates are accurate on average, then
the winner will be approved by approximately fifty percent of the voters.

In all three of the cases considered the fifty percent approval quota
seems reasonable.

If CR ballots are used and the approval cutoff is indicated by rating a
fictitious candidate MAC (minimum acceptable candidate) or NOTB (none of
the below), then fifty percent approval of some real candidate just means
that as many voters as not considered the candidate better than having to
start over with a new set of candidates, i.e. the real candidate beat the
fictitious candidate head-to-head.

[The default rating of the fictitious candidate, i.e. the default approval
cutoff would be the CR midrange value.]

So perhaps the fifty percent approval quota is not quite as arbitrary as
some other quota would be.

In standard Approval there is no quota.

If there were a fifty percent quota, how would you want to use it?

Demorep used to suggest searching for a Condorcet Winner among all of the
candidates that had at least fifty percent approval. Then in the case of
no CW, going with the candidate having highest approval.

Alternatively, one could have an approval runoff among the candidates with
at least fifty percent approval: the CR scores on the ballots could be
used to infer the voters' wishes for the runoff approvals, for example.

Is there some other way to put this 50 percent approval information to
work, or is it just a curiosity?

In any case, it seems that if the winning candidate gets much less than
fifty percent approval, either the voters are using bad strategy or else
the candidate field is so lousy that the winner should have some official
restriction due to lack of mandate.

All of this would depend on the type of election (i.e. the application of
the method), of course.


On Fri, 18 Apr 2003, Forest Simmons wrote:

> Note that if every approval voter approves at least one of the two
> front runners, then at least one of them will have 50 percent approval or
> more, so it looks like it isn't too far fetched to expect or require 50
> percent or better approval for the winner.
> Also, optimal zero information strategy tends to give the winner more than
> fifty percent approval about fifty percent of the time, given a uniform
> distribution of voter utilities for the candidates.
> Forest
> ----
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