[EM] Two Paramount Criteria

[Forest Simmons]

For me two paramount criteria are

(1) simplicity of optimal or near optimal strategy, and

(2) as much voting power as possible consistent with (1).

There are various possible definitions of "voting power," but it should
have something to do with the probability of one ballot or set of ballots
being pivotal to the outcome in an election chosen at random from some
family of elections.



Here's a method that comes close to satisfying these criteria:

The method takes ranked ballots with equal rankings allowed, as input.

The method first applies Rob LeGrand's "ballot-by-ballot" version of
"strategy A" to all possible permutations of the ballot. [Yes, this method
is computationally intractable.]

If the same candidate wins for all permutations, then that candidate is
declared winner.

Else, Joe Weinstein's weighted median method is applied to determine the
winner.  A candidate's weight is the number of permutations that it won
(according to Rob) plus one (so that each candidate has non-zero weight).

Although this method is computationally intractable,the method winner can
be calculated with 99.9 percent accuracy without inordinate computational
burden, by use of montecarlo methods, for example.

The residual doubt is small compared to other sources of doubt in other
voting methods, especially the doubt that the votes were sincere, or the
doubt that the the voters were using their best strategy for maximizing
their voting power.

Note that the method is completely deterministic, but that practical
estimation of the method's winner may require something like montecarlo.

Perhaps the voters could get use to such an idea if they could see the
advantages of satisfying criteria one and two above.

Forest