Approval strategy

[MIKE OSSIPOFF]

Adam was quoted:

>Adam was more helpful, with a rule I could follow: Approve whichever 
>candidate I prefer among the expected front runners, and approve all the 
>candidates I like better than that one.

That's an easily-applied strategy, since one thing oftenr relatively
obvious is who the 2 strongest contenders are. The above strategy
of course is the one that voters use in Plurality.

Say we call the two strongest contenders X & Y.
It can be fancied up a bit, though. Say the top-2 are equally
likely to be the one that outpolls the other. Then, for any other
candidate Z, if Z managed to get into a tie for 1st, Z would be
equally likely to tie X & Y. So Z should be approved if Z is
better than the halfway point between X & Y. That's the strategy
described in an journal article that someone once sent me a copy of.
I don't remember the authors.

We can get a little more elaborate if we estimate the probability
that X will outpoll Y, or that Y will outpoll X. If there's a 70%
chance that X will outpoll Y, then Z is correspondingly more likely
to be in a tie for 1st with X than with Y. Those probabilities
for Z, and Z's utility relative to X and to Y, can be used to
decide whether we should approve Z. Of course we're talking about
some Z whose utility is somewhere between that of X & Y.

Of course now we're judging Z by his relative chances of tying
X or Y, but we're ignoring the smaller chance of 2 candidates other
than X or Y tying eachother.

That would be the next natural step, then, in a smooth gradation
in elaboratenes: Having identified the 2 strongest contenders,
and estimated their probabilities of outpolling eachother,
write how likely each is to win, and
consider how less likely to win are the other candidates. That's
a small additional task. Then we have the Wi, the win probabilities
that Weber-Tideman uses.

Mike Ossipoff




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