[EM] Rewording Strategy A (BF(1st))

[Forest Simmons]

> From: "MIKE OSSIPOFF" <nkklrp at hotmail.com>
> 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.


Forest