> > I'm afraid I said it backwards..."above" and "below" need to be switched > to make it right! > Date: Wed, 2 Dec 2020 14:56:34 -0800 > From: Forest Simmons <fsimmons@pcc.edu> > To: EM <election-methods@lists.electorama.com> > Subject: Re: [EM] Copeland Done Right > > 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. > ************************************************ >