From: "MIKE OSSIPOFF" <[EMAIL PROTECTED]> Subject: [EM] Rewordng strategy A (BF(1st))
The strategy that's been called Strategy A, and which I've been calling BF(1st) has been worded like this:
The Approval cutoff point goes adjacent to the candidate expected to get the most votes, toward the side of the candidate expected to get the 2nd most votes.
[end of Strategy A definition]
But that could be reworded in a way that makes it obvious that it's a Best Frontrunner version:
The Approval cutoff is between the two expected frontrunners, and is adjacent to the one that is expected to outpoll the other.
[end of suggested rewording of BF(1st)]
This wording is the best I've seen for introducing the concept, but it doesn't tell what to do when (1) neither of the two frontrunners is preferred over the other by the voter, or what to do in the case (2) when the two frontrunners are considered equally likely to win.
So after introducing the concept as you have done we could treat these borderline cases as follows:
First identify the candidate X that you think is most likely to win, i.e. the "frontrunner."
Then if some candidate that you like less than X has a greater chance of winning than any candidate that you like more than X, then put the cutoff just below X, else above.
That takes care of case (1).
In case (2) the approval cutoff should be halfway (in utility, if known) between the two frontfunners, unless the voter has no preference between them, which would put us back in case (1), which we have already covered.
The bad part of this case (2) is that (unlike case 1) we need to estimate the average utility of the two frontrunners.
Departing from Strategy A, we offer the following refinement in the same spirit:
For each candidate C, if you think the winner is more likely to come from the set of candidates that are worse than C than from the set of candidates that are better than C, then approve C, else don't.
This neatly takes care of all of the cases, and agrees with Strategy A whenever there are two definite frontrunners.
Perhaps if Russ were to study this strategy he would see the continuity between the two dominant party case and the general case that he is worried about.
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