[EM] a similar method to weighted pairwise

[James Green-Armytage]

	It occurred to me that there is another method which is similar to
weighted pairwise, which uses an approval cutoff rather than a cardinal
ratings ballot. 

Ballots:
ranked ballots with approval cutoff

Tally:
1. Pairwise tally using the ranked ballots. Elect the Condorcet winner if
one exists.
	If there is a majority rule cycle:
2. Using the ranked ballots only, construct a map of which candidates beat
or tie other candidates. At this point we are only determining the
direction of the defeats, not the magnitude.
3. For a given defeat A over B, the magnitude of the defeat is defined by
the number of voters who place A above their approval cutoff and B below
their approval cutoff.
4. Using this definition of defeat strength, you can resolve the cycle
with methods such as minimax, beatpath, or ranked pairs.

	Perhaps this method has already been proposed? I haven't heard of it
specifically, but I know that people on the list have done a lot of work
with approval cutoffs.
	This method requires a ballot that is arguably simpler than weighted
pairwise, i.e. rankings plus an approval cutoff. It is also likely to
produce similar results in many cases. However, it is by no means an
identical method. This method does not allow voters the full range of
expression which is the intended purpose of weighted pairwise, that is,
the ability to have more than one utility gap. At present, I prefer
weighted pairwise.


James Green-Armytage