[EM] Why Approval & CR are equivalent

[MIKE OSSIPOFF]

It's really easy to show that, in public elections, where there are
many voters, Approval and CR are strategically equivalent.

Of course voting strategy for maximizing your expectation depends
on the fact that your voting might change the outcome, and that,
therefore it can be said that your ballot changes probabilities.

But, in public elections, your ballot doesn't change any probabilities
enough to change the probability assumptions that your strategy is
based on.

Say it's a CR election, and you decide how to mark your ballot as
follows:

First, dedide which candidates whould get a first point, on the
basis of what allotment of first points to the candidates would
maximize your expectation, based only on those 1st points. Of course
that's  Approval strategy.

Now, after you've done that, decide which candidates should get
a point in addition to whatever you've given (or not given) them.

Since we can safely assume that your votes don't change the probabilities 
enough to change your strategy, your point allotment
in this 2nd round will be exactly the same as in the 1st round.

Likewise for each subsequent round, including the one in which you
give some candidates the maximum number of points allowed.

So, the candidates you'd vote for in Approval get maximum points,
and the candidates you wouldn't vote for in Approval get minimum
points.

I don't know if that equivalence exists in small committee elections.

Mike Ossipoff





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