Kevin, You wrote (Wed.Mar.31):
To avoid the need for approval cutoffs, why not use the plain Weighted Mean Approval scores to set the fixed elimination schedule, and then the rest is like fractional IRV with a majority stopping rule ?A method I would rank between Condorcet and Approval is AER, or "Approval STV." It's IRV, but the elimination order is based on approval. Because the approval counts don't change, and the elimination order is thus fixed from the beginning, it's monotonic. It's intuitive, and gives similar results to WV methods.
Weighted Mean Approval .
Voters rank the candidates, equal preferences ok.
Each candidate is given a weight of 1 for each ballot on which that candidate is ranked alone in first place, 1/2 for each ballot on which that candidate is equal ranked first with one other candidate, 1/3 for each ballot on which that candidate is ranked equal first with two other candidates, and so on so that the total of all the weights equals the number of ballots.
Then approval scores for each candidate is derived thus: each ballot approves all candidates that are ranked in first or equal first place
(and does not approve all candidates that are ranked last or equal last). Subject to that, if the total weight of the approved candidates is less than half the total of number of ballots, then the candidate/s on the second preference-level are also approved, and the third, and so on; stopping as soon as the total weight of the approved candidates equals or exceeds half the total mumber of ballots.
Chris Benham
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