Everything works fine if we replace the random ballot distribution with an estimate of winning probabilities not determined from the rankings.
A discussion of how to do that is beyond the scope of this message, but a quick and dirty way would be to have the voters indicate which of the alternatives they consider to be viable, and make the respective probability estimates proportional to the number of viability marks.
With that adjustment we can restore the original symmetry of Joe Weinstein's rule. The DSV version of approval based on rankings becomes... for each ballot B and each alternative X, approve X on B if and only if the alternatives ranked strictly above X on B have greater total winning probability than those ranked strictly below X.
Now for de-cloned Copeland: The de-cloned Copeland score of alternative X is the sum of the probabilities of the alternatives pairwise beaten by X minus the sum of the probabilities of the alternatives that beat X pairwise. The alternative with the highest score is declared winner!
Notice that if X covers Y, and Y has positive probability, then X has a greater score than Y. In other words this version of Copeland preserve the Landau property: it always elects uncovered alternatives.
On Wednesday, December 2, 2020, <[hidden email]> wrote: ...
Election-Methods mailing list - see https://electorama.com/em for list info
|Free forum by Nabble||Edit this page|