Benham's method: Difference between revisions

A variation of Benham's that addressesis defined in reference to the Smith set rather than the Condorcet winner is "Do IRV, but before each elimination eliminate all candidates outside the (smallest group of uneliminated candidates such that all candidates in the group pairwise beat all (uneliminated) candidates outside of the group), and repeat until only one candidate remains, who is the winner." This would pass ISDA, since to begin with the voting method eliminates everyone not in the Smith set. It is equivalent to [[Smith//IRV]] when there are only 3 candidates in the Smith set, since both methods will eliminate everyone outside of the Smith set, then eliminate one of the 3 candidates in the Smith set, resulting in either a pairwise tie between the two remaining candidates (thus both are tied in IRV/ in the Smith set) or one pairwise beating the other (and thus receiving a majority under IRV/being the only member of the shrunken Smith set). An example where they would differ go as follows: suppose the Smith set has 7 candidates. Both methods would eliminate everyone but these 7, then would eliminate the same candidate out of the 7. Now suppose there are 3 candidates who form their own Smith set when ignoring their pairwise matchups against the just-eliminated candidate; Smith//IRV might eliminate all 3 of them and elect someone else, whereas the Smith-defined variation of Benham's would eliminate everyone but the 3 and thus guarantee one of them wins.