Mike's exposition of basic Approval and Range strategy as variations on the
theme of Better Than
Expectation strategy was very interesting and valuable, including the
recommendation of introducintg
Approval after score or grade voting, which are much more familiar to most
people.
That was probably the most important part of his message, but I want to make a
few more remarks about
Approval strategy.
1. When there are candidates between the two front runners and you are not
sure where to draw the
approval line, put it adjacent to the candidate with the greatest likelihood of
winning. In other words put your
approval cutoff adjacent to the candidate most likely to win on the side of the
candidate next most likely to
win. This is what Rob LeGrand calls "strategy A."
2. Suppose that order is easier than ratings for you. Joe Weinstein's idea is
to approve candidate X if and
only if it is more likely that the winner will be someone that you rank behind
candidate X than someone that
you rank ahead of candidate X. Note that when there are two obvious
frontrunners Joe's strategy reduces to
Rob's strategy A.
3. Suppose that on principle someone would never use approval strategy on a
score/grade/range ballot, but
is forced to use an approval ballot anyway. How could they vote as close as
possible to their scruples?
For example suppose that you would give candidate X a score of 37 percent on a
high resolution score
ballot, but are forced to vote approval style. In this case you can have a
random number generator pick a
number between zero and 100. If the random number is less than 37, then
approve the candidate,
otherwise do not. If all like minded voters used this same strategy, 37
percent of them would approve
candidate X, and the result would be the same as if all of them had voted 37 on
a scale from zero to one
hundred.
Now for the interesting part: if you use this strategy on your approval
ballot, the expected number of
candidates that you would approve is simply the sum of the probabilities of
your approving the individual
candiates, i.e. the total score of all the candidates on your score ballot
divided by the maximum possible
score (100 in the example). Suppose that there are n candidates, and that the
expected number that you
will approve is k. Then instead of going through the random number rigamarole,
just approve your top k
candidates.
Forest
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