> Juho wrote: > >> How about "the smallest number of ballots on which some >> alternative that beats A pairwise is ranked higher than A"? >> >> Juho
If I am not mistaken, this idea is equivalent to electing the alternative A with the greatest number of ballots on which A is ranked higher than any alternative that beats A pairwise. Here's a variant that could be used with cardinal ratings/range ballots: Elect the alternative A with the greatest number of ballots on each of which A is rated above the expected rating of the alternatives that beat A pairwise. This, in turn, leads to a variant of an old method of Chris Benham's and mine (what did we call it?). In that method on each ordinal ballot each name was replicated as many times as there were ballots on which that name was ranked first. Then an approval cutoff was placed halfway down the beefed up ballot. The variant I am suggesting would only beef up the candidates that beat A pairwise. Then elect the alternative A that has the most ballots on which it is ranked above the halfway mark of its beefed up version. Example: 5 ABC, 4BCA, 3CAB. C beats A, and C is ranked first on three ballots, so A's beefed up ballots are 5 ABCCC, 4BCCCA, 3CCCAB A is above the halfway mark on only the first five of these, so A's score is 5. Similarly, B 's beefed up ballots are 5 AAAAABC, 4BCAAAAA, 3CAAAAAB So B's score is 4. Similarly, C's beefed up ballots are 5 ABBBBC, 4BBBBCA, 3CABBBB So C's score is 3. So A's score of 5 is the highest.
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