[EM] extending Myerson's test--more policy positions

[Blake Cretney]

On Fri, 17 Mar 2000, "MIKE OSSIPOFF" wrote:
> > >
> > > David Catchpole wrote:

> > > I wonder what strategy is optimal under a pairwise system?  Should The 
> >optimal strategy when no strategy info is available, for a Condorcet
> >completion system, is sincere expression of preferences... Anyone dare to
> >argue? Huh? I would feel that any additional strategy brought about by
> >extra information would depend on the completion.
> 
> When nothing is known about CW or median, then maybe one would
> want to rank all candidates, or cautiously only rank the
> best ones. With most pairwise methods, you might also want to
> feel cautious enough to rank a number of the best ones at 1st
> place, just to be safe against the others. (but not with Condorcet).

I would hypothesize that in IRV, standard Borda, and all forms of  Condorcet that use margins of defeat, the best strategy with zero information is a sincere vote.  Although, it is unclear how equal votes are counted in IRV, except at the end of the ballot, and this would make a difference.  I'm not going to address that, however.

Let's assume you have the following preference, and you are using a Condorcet method that is equivalent to Minmax (margins) with 3 candidates.

A 100
B 90
C 0

Your sincere preference is
A>B>C

If you voted
A=B>C

Then, if the real fight is A vs. B, you may lose out by not expressing your preference.

You may be helped if the fight is B vs. C, and you decrease B's loss, but there is an equal chance that you will be hurt by an A vs. C comparison, where you fail to decrease A's loss.

So, there seems to be no zero-knowledge strategy that would cause you to rate candidates together in first place.  A similar argument can be made against equal rankings and order-reversal elsewhere in the ballot.

I don't know the full answer for Minmax (winning-votes), but it seems clear that at least in some situations the best zero-knowledge strategy will be not to express rankings between the most preferred candidates.  In the example given, you would have to weigh the disadvantage of not being able to express a preference between A and B, vs. the advantage of lowering the chance of a victory by C.  The preference A>B will tend to increase B's loss more than it will decrease A's loss, so expressing the preference will tend to make C more likely to win.  The trade off is similar to the one in Average Ratings and Approval.

It's possible, that your best strategy is to rank equally all candidates with above-average utility, but I'm not sure.  You certainly wouldn't want to rank candidates equally towards the end of your ballot, as this would increase their likelihood of winning.

---
Blake Cretney