[EM] Some Voting Tables

[Bart Ingles]

Richard Moore wrote:
> 
> Forest Simmons wrote:
> 
> > Here's an example that turns out to be more interesting than it first
> > appears to be:
> >
> > (Sincere intensities or utilities are in parentheses.)
> >
> > 45  A(100) B(50) C(0)
> > 30  B(100) C(50) A(0)
> > 25  C(100) A(50) B(0)
> 
> ...
> 
> > In this "zero information" case Approval voters have to decide whether to
> > use above mean inclusive strategy or above mean exclusive strategy. i.e.
> > should they approve their mean candidates or not?
> 
> In true zero-info cases, it's above mean (exclusive). There's no basis for
> believing that any particular candidate has a better chance than any other,
> given the lack of information, and ignoring your own ballot. So you assume
> all candidates have equal chances. But, when you consider your own ballot,
> which will certainly include your favorite, the scale is tipped, ever so
> slightly, towards your favorite. So there's no incentive to vote a second
> choice if that choice is right on your approval threshold.
> 
> This strict zero-info strategy leads to A winning.
> 
> With large populations, your first choice is already diluted so that the
> effect of your second choice on the expected utility of the outcome is
> negligible. In such cases you could just as well flip a coin over your
> middle choice. But with a small number of voters, the first-choice effect
> is significant.

I'd thought for some time that above-the-mean strategy would be
preferable, but for slightly different reasons.  Not 100% sure of my
reasoning, but here goes:


If we assume that one of the candidates is ahead -- that is, has a
significantly higher than average number of supporters -- then a given
voter should have a better-than-average chance of being among those
supporters.  And if you believe that your favorite is a front runner,
then there incentive not to approve of additional candidates.

Considering the reverse -- that one of the candidates is disliked by a
larger share of the voters, then this candidate will probably lose
without the need for compromise votes for some other lesser-evil
candidate.


It would be interesting to try to quantify the expected spread -- say as
a percentage of votes typically received by _any_ winning candidate. 
Then for a randomly-chosen voter, the probability of belonging to the
winning faction should be the same as this percentage.  You could then
calculate a better-than-random strategy for this voter with no other
evidence about the candidates' poll standings.