[EM] Most Tolerable or Better

[fsimmons at pcc.edu]

What about strategy for "Most Tolerable of Better?"

In ordinary Approval, the strategy S that maximizes the probability of being
pivotal (in the desired direction) is to approve alternative X if and only if X
is less likely to be tied with an alternative that you prefer over X than it is
with an alternative that you like less than X.

When most of the winning probability is concentrated in only two alternatives,
this strategy reduces to Rob LeGrand's strategy A:  put your approval cutoff
adjacent to the alternative most likely to win on the side of the alternative
with the next greatest winning probability.

Suppose that there are two lesser evils X and Y running about even in winning
probability with the candidate Z that you detest the most (anybody but Z).  Do
you approve both lesser evils X and Y, or just the one X that that you have a
slight preference for?

Under ordinary approval, this is a difficult question, since the probabilities
involved are apt to be pretty rough estimates, and it may be that your preferred
compromise X is just short of the necessary support to beat Z.

[If you use the strategy S that maximizes the probability of being pivotal (in
the desired direction), then you approve Y if and only if Z has a greater
probability of winning than X.  But these two probabilities are not precisely
known.]

Under "Most Tolerable or Better" you can mark X and Y as better and tolerable,
respectively, while leaving Z at the default bottom.  This maximizes the chance
that Z will not win, and contributes to X over Y in the not too unlikely case
that X and Y end up with the same tolerable or better score ahead of Z.

You might say that these ties are too unlikely to matter, but where there is no
tie or near tie, your ballot cannot be pivotal anyway.