[EM] Copeland done right

[Forest Simmons]

>
>  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 at pcc.edu>
> To: EM <election-methods at 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.



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