[EM] A note on Approval strategy A.

[Simmons, Forest]

Suppose that the approval results from a reliable poll are published as follows:
 
2 %  approve A only.
25 % approve both A and B
23 % approve C only.
 
And now it's your turn to vote an approval ballot.
 
According to approval strategy A, you should put your approval cutoff on the B side of A (in your mental ordering of the candidates), since A is the approval frontrunner, and B is the runner up.
 
But note that (in the sample) every ballot that approves B also approves A.  If this is a real feature of the population, it will be impossible for B to get more approval than A.
 
So it appears that even though C has less approval than B at this point, C is a bigger threat to A than B is.
 
I think I would put my approval cutoff on the C side of A.
 
Moral of the story.: when you have information about how candidate approvals are correlated on the previous ballots or on approval polls, then approval strategy A, which does not take that information into account, may be inadequate.
 
How can one make use of the correlation information in general?
 
If nothing else, it is easy to approximate the winning (and tie for first place) probabilities by repeated Montecarlo simulations based on the distribution of the approval ballot profiles in the poll.
 
Forest
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