[EM] a method based on candidate separation

[Forest Simmons]

Ross Hyman recently suggested a method that eliminates the pairwise loser
of the bottom remaining candidates on a list (in his suggestion the list
was a random ballot order) as long as there remain two or more uneliminated
candidates.


It got me to thinking that ideally we would eliminate the pairwise loser of
the two candidates with the most separation in issue space.

The problem with that idea is that we have no direct way of measuring how
far apart candidates are in issue space.

The voters could be polled on their views not only of the candidates but of
the issues, and then the candidate positions could be inferred from the
average positions of their respective supporters.

Alternaively, in the case of range ballots one could estimate the relative
distances apart in candidate space by computing the following correlation
score for each pair (A, B) of candidates:

score(A, B)=Sum (over ballots i) of A(i)*B(i),

Where A(i) and B(i) are the respective candidate ratings on ballot i.

The lower the score for the pair the further apart the two candidates.

So while two or more candidates remain, eliminate the pairwise loser of the
pair with the greatest separation.

Of course, this requires cardinal ratings style ballots, but for large
elections implicit approval might be enough: A(i) = 1 or zero depending on
whether or not candidate A is approved on ballot i.

For that matter implicit approval could be used.

I don't suggest this as another public proposal, but for use as a standard
of comparison like MAM, when range style ballots are used.

Forest
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