You recently asked for opinions of this Condorcet completed by Approval Elimination method:
"The voters rank the candidates and also specify an Approval cutoff. The CW wins if one exists, otherwise the least approved candidate is repeatedly eliminated until a CW is obtained."
I agree that for something with such a short and succinct description, this method is pretty good.
But I'm surprised that you think that the "sound byte" advantage overcomes the extra complication of having
an approval cutoff.
That issue aside, I prefer another method that uses that type of ballot, "Approval Margins":
(1) Voters rank the candidates and also give an Approval cutoff
(2) Eliminate non-members of the Schwartz set, and then "move" the approval cutoffs on those ballots that
either approve all or none of the remaining candidates the minimum distance so that they now approve or not approve
at least one of the remaining candidates.
(3)Determine the winners and losers in the pairwise comparisons among the remaining candidates (the directions of the defeats)
purely by the rankings, but determine their "weights" by the the margins between the candidates' pairs of Approval scores.
(4) On that basis use Ranked Pairs or Beat Path or River to pick the winner.
Some people might be in favour of simplifying it by omitting step 2.
An old example given by Adam Tarr. Sincere rankings: 49 R>C>L 12 C>R>L 12 C>L>R 27 L>C>R C is the CW.
Suppose there is pre-polling and so the L supporters decide to approve C, while the C supporters sincerely divide their approvals.
Further suppose that the R supporters all decide to completely Bury C. Then we might get:
49 R>L>>C 06 C>R>>L 06 C>>R>L 06 C>>L>R 06 C>L>>R 27 L>C>>R
Now all the candidates are in the top cycle: L>C>R>L. The approval scores are L82, R55, C51.
The Approval Elimination method you propose eliminates C and elects the Buriers candidate R.
Approval Margins: L>C 82-51 = +31 C>R 51-55 = -4 R>L 55-82 = -27
The "weakest defeat" is L's (by an margin of negative 27), so the Burying backfires and L wins!
Chris Benham
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