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

[Bart Ingles]

David Catchpole wrote:
> I'll announce the approval/cumulative voting strategy that I think is
> useful for voters with little information about other voters. There are n
> candidates. Vote for the n/2 or n/2 + 1 candidates you most prefer.
> 
> Any other suggestions?


The proven optimal strategy when no strategy info is available is to
vote for candidates for whom the voter gives above-average utilities
(above average for the field of candidates).  You could probably fudge
the threshold upwards, since the voter has a slightly higher probability
of favoring a popular candidate than an unpopular one, thus should
probably vote for fewer candidates.

Your strategy of voting for n/2 candidates might be an easy heuristic,
but if you want to use it I would add an exception for candidates whom
the voter rates very high or very low.  So a quick and dirty rule might
be something like "...vote for the half of the candidates you like best,
but always vote for a candidate rated above 8 or below 2 on a scale of
0-10...", where the 8 and 2 figures would be replaced by whatever
numbers best approximate the curve for the average utility formula.

I haven't seen or heard of many U.S. elections that lacked 1 or 2
front-runners, though, so I expect this would generally be unnecessary. 
You would expect partisan elections to have 2 front-runners when there
is a two-party system, but even non-partisan and primary elections here
generally seem to have front-runners.

  *  *  *

I wonder what strategy is optimal under a pairwise system?  Should you
refuse to rank candidates whom you rate below a certain number?  If your
favorite is one of two known front-runners with a 50-50 chance of
defeating the other front-runner, it would seem advantageous to refuse
to rank anyone whom you would rate below the middle of the scale.

Does this sound valid?  If so, is there a corresponding strategy for
candidates you would rate above a certain level, e.g. should you rank
some of them as equal to your favorite?  This seems less likely, but I
wonder if anyone has calculated the optimal strategies for
utility-maximizing voters.  I'm ignoring the possibility of using
order-reversal here for simplicity.