[EM] Score MCA, or MCA Score

[Jameson Quinn]

>
>
> But Approval has been criticized for the co-operation/defection
> problem. In fact, that problem is the subject of the "Approval
> bad-example" that I've discussed at EM.
>
> That problem can happen, but Forest Simmons proposed an excellent
> solution to it. Forest suggested what I call "strategic fractional
> ratings" (SFR). In the Approval bad-example where the A voters and the
> B voters greatly prefer A and B to C, and despise C, but want their
> own candidate to be the {A,B} candidate who wins, and if you're an A
> voter, and you know that the B voters would like to take advantage of
> your co-cooperativeness if you approved B, then you could give to B a
> _fractional_ rating, by probabilistically approving B. Approve B with
> probability that is effectively like giving B a fractional Score
> rating. Draw a numbered piece of paper from a bag, for example.
>
> The idea is to give to B just enough so that B will be able to beat C
> and win, only if the B voters are more numerous than the A voters.
> After all, if B is bigger, then you don't mind helping B win for you.
> B is then the rightful winner in {A,B}. But you don't want to help B
> win if B is smaller than A, and the less-numerous B voters are taking
> advantage of your co-cooperativeness. Hence SFR.
>

This approach was formalized in Bouton, L., and M. Castanheira. “One
Person, Many Votes: Divided Majority and Information Aggregation.” *
Econometrica* 80, no. 1 (2012): 43–87. Apparently since then they've done
some yet-unpublished empirical work to see if people really vote that way
if the conditions are right; and found that they partially do.

Jameson
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