[EM] Martin Harper Approval Runoff (was STAR)

[Forest Simmons]

This method seems to be the  simplest Approval Runoff adequate for a very
large single seat election.

Martin Harper suggested that after the approval ballots have been tallied
in the usual way, each ballot B be designated as a vote for that candidate
C=V(B) (among those approved on B) with the most total approval from the
other ballots.

Candidate X's transferred vote count TVC(X) is then defined as the number
of ballots B such that X=V(B).

In other words ...

TVC(X)=#{B|V(B)=X}.

The MHAR runoff is between the two candidates with the greatest Transferred
Vote Counts.

Martin Harper showed that absent a tie, the approval winner will have the
largest TVC ... which implies that the candidate with the top approval
count will automatically be one of the runoff finalists.

For a three candidate runoff, let X, Y, and Z be the three respective
candidates with greatest Martin Harper Transferred Vote Counts.

Elect the winner of the sincere runoff represented by the expression

X vs (Y vs Z)

Rational voters that are aware of the true preferences of the other voters
regarding these finalists will elect the sincere CW if there is one ...
otherwise they will elect the approval winner.

fws
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