[EM] Automated Approval methods (was Single Contest)

[Kevin Venzke]

Hi,

My Single Contest method takes advantage of the voters' agony over having
to place an approval cutoff, by using their decisions to guess at the
most important pairwise contest, and using only that one. This results
in a minimum of possible strategies to use on the ranking side.

It's in pursuit of this goal that the method is a "single contest" 
method, and not an automated approval cutoff relocator.

But, it is interesting to consider getting rid of the explicit approval
cutoff and just using ratings. The tricky thing is that now the voters
don't tell us which contests they guess are important (that is, if they
are voting sincerely), so to do a single contest method we have to 
guess.

(Actually, since the voters aren't even the ones placing the cutoff, I
am not too sure there is anything to be gained by having it be a
single contest method rather than an automated approval cutoff placer.)

Here's my first attempt, which I called VVAA (viability times value
automated approval): Find the pair of candidates that maximizes this
figure:

the number of ballots favoring the pairwise loser of the two
times
the worse of the two Range scores.

Either use this pair as the single contest, or use the two candidates
to find an approval cutoff for each ballot, and elect the approval 
winner.

Here is my thinking: The perceived most important contest has to be
1. pairwise competitive
and
2. competitive with other pairs. I am not too sure how to word this.
Basically AB shouldn't be the top pair if all B voters prefer C to B. 
I approximated this by looking at the Range scores, but that seems iffy.
(This method wasn't that great, for one thing, but the Range measure 
also doesn't seem to emulate any realistic process.)

In *most* elections I would say to look at who was ranked vs. not 
ranked. But if you want to at least pretend that voters will feel free
to vote for all the candidates, you should have votes for everyone, and
you have to e.g. decide what to do when there is a voted CW with very 
low voted utility. Should he be in the pair? Is that realistic? Does 
it matter?


I also tried implementing the most obvious (I suppose) method: Take the
ratings and conduct simulated approval polling, either for some
determined or semi-random number of iterations, or until someone wins
twice in a row. This doesn't test as well as I thought it would though.

Kevin Venzke