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

I should add that if the second highest transferred vote count is less than two thirds (say) of the highest count, then no runoff is needed. On Sat, Aug 19, 2023, 10:16 PM Forest Simmons <forest.simmons21@gmail.com> wrote: > 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 >