[EM] Approval Strategy, SODA, SARA, etc.

[Forest Simmons]

The inspiration for Yes/NoCandidateProxy, SODA, MAS, SARA, etc. was
fundamentally this:

Approval voters tend to have a top set that they definitely approve, and a
bottom set that they definitely disapprove.  The question is what to do
with the rest, the "indefinite set" between Top and Bottom.

As Michael has pointed out there are various strategies that work in
various contexts, and the current USA context would not require anything
sophisticated.

Here's a strategy that I have been thinking about that could be automated
as a DSV system, but is simple enough that it could be recommended for use
by the man (or woman) behind the plough (as Charles Dodgson put it).

The context is an Approval election with partial but not too reliable
information about winning probabilities.

1.  Approve all candidates that you definitely approve, i.e. all candidates
in your "top set."

2.  Leave unapproved all of the candidates in your "bottom set."

3.  Approve p percent of the remaining indefinite set, where p is given by
the formula  (1 + pB - pT)/2 , where pB is your subjective estimate of the
pobability that someone from your bottom set will be elected, and pT is the
probability that someone from your Top set will be elected.

So if pB=pT, the formula recommends that you approve half of the remaining
candidates.   If pB>pT you will approve more than half of the remaining
candidates.  If pB<pT you will approve fewer than half of the remaining
candidates. If pB=0, and pT = 1,then it recommends that you approve none of
the remaining candidates   If pB=1 and pT=0, it recommends that you approve
all of the remaining candidates.

This formula follows from the "approve above expected merit" method in the
context where the candidates in the indefinite category are distributed
uniformly between zero and one in merit.  But it is so robust that it
should give good results even if that assumption is only approximately
true.

One can always follow one's gut feeling when in doubt.  If the method
recommends that you approve seven candidates and you are feeling doubtfull
about the worst of the seven, then by all means (and medians) leave that
one unapproved.

Other guidlines that involve a sense of who the CWs is, or which candidate
are below the merit midrange can help inform borderline cases.

Of course, if you have enough information to know that the distribution of
merit among the indefinite candidates is no where near uniform, then you
have enough information to use a better decision method, like approve above
expected merit.

Thanks,

Forest
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