[EM] re: CR/Approval and cutoffs

[Forest Simmons]

On Wed, 1 Oct 2003, [iso-8859-1] Kevin Venzke wrote:

> Forest,
>
>  --- Forest Simmons <fsimmons at pcc.edu> a écrit :
> > If the average were actually the true expectation of the outcome (not
> > counting your ballot) then you should vote strictly above average.
>
> I'm not so sure about this.  Suppose we're talking about strategy for a method
> called "Disapproval."  Wouldn't the proper strategy be "Disapprove every candidate
> worse than your expectation for the election"?  It seems to me that optimal strategy
> tells us nothing about what to do with candidates on the average, and I think it's
> because there's no good or bad advice either way.

If the true expectation without your vote is exactly r, and you approve
strictly above r, then you raise the expectation to some number r + delta.

Then if (as an after thought) you also approve at the level r, this brings
the expectation down to some value between r and r+delta.

Note that this argument assumes tacitly that r is not the max CR level.
If r is the max CR value, then you might want to approve at level r to
increase your confidence in the expected value, and to show your support.

On the other hand, if your CR values only reflected the best in a poor
pool of candidates, you might want to approve nobody in order to show your
disdain.

This could make a fig's worth of difference if there were many like minded
voters.  In other words, publishing the expected value could influence the
voters behavior in such a way as to change the expected value.  To play
it safe it is best to approve all top rated candidates, unless the
expression of disdain has a higher expected utility than the expected
utility of the election (for you).


> Supposing that one only approves above expectation, it should be just as likely
> that we cause an expectation-level candidate to lose to someone worse, as to keep a
> preferable candidate from winning were we to approve the expectation-level candidate.

Perhaps so, but on average you will do better to approve only above
expectation, if the expectation has not been miscalculated, and if there
are any levels above the expectation level containing candidates with any
chance of winning.

It seems to me that you are willing to make an infinitesimal sacrifice in
expectation in order to decrease (ever so slightly) the standard
deviation.

Would you rather put a nickel into a machine that gives back a dollar on
average with standard deviation of a nickel or into a machine that gives
back $1.01 on average with a standard deviation of a dime?


> The bottom line, for me, is that it would not be good to have every voter
> disapprove the candidates at their expectation level.

Evidently you are not including the case of zero expectation.  If no
candidate above the bottom level had any chance of winning, you would
still want to vote strictly above zero even though it wouldn't "make a fig
of difference" in the outcome of the election.

Forest