[EM] Condorcet methods - should the cycle order always determine the result order? (Toby Pereira)

[Toby Pereira]

Kemeny certainly wouldn't be my preferred choice, partly because of its lack of clone independence, but I mentioned it because it seems to come up frequently enough.

I think I remember seeing before your "done right" post. I'll have to read it again, because I remember considering the possibility of a cloneproof Borda before and deciding that any attempt to cloneproof it would leave it unrecognisable from Borda. For example, if you have the following ballots:

10: A>B>C>D>E
10: B>C>D>E>A

Using Borda philosophy, B is the best here, but from the perspective of A, BCDE form a clone group, so any cloneproof system would have to consider A equal to each other candidate.

I think cloneproof Condorcet systems wouldn't have a set order here. While they would rank B>C>D>E, there would be no specific place for A to go. And I think this is why (as people have said), Condorcet methods don't necessarily have a complete fixed order. For example, even though B beats C and A is equal to C, it is not the case that B beats A.

But back to Borda - if the cloneproof version of Borda uses scores (as normal Borda does), then I can't see a set of scores that would make sense here. We can have scores so that B>C>D>E. But any score for A doesn't work. Because A has to be equal to all of them!

But this also makes me wonder generally - are there any sensible cloneproof ranked-ballot systems that aren't Condorcet methods? IRV is cloneproof, but is it sensible? Is there anything else?


>________________________________
> From: Forest Simmons <fsimmons at pcc.edu>
>To: EM <election-methods at lists.electorama.com> 
>Sent: Tuesday, 4 November 2014, 22:46
>Subject: [EM] Condorcet methods - should the cycle order always determine the result order? (Toby Pereira)
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>
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>Toby,
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>You mentioned Kemeny.  The very purpose of Kemeny is to determine a "social order," namely the one that minimizes the average "distance" from that order to the ballot orders..
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>The trouble with Kemeny is that the choice of metric for the "distance:" is clone dependent: changing the size of a clone set changes the number of transpositions of order to move a candidate past that set. 
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>However, if cardinal ratings (e.g. score ballots) are used, then clone independent metrics can be substituted for the Kemeny distance. I once posted a message to this list describing a clone free technique for converting a set of ordinal ballots into a set of ratings  Then based on those ratings it was possible to define "Kemeny Done Right,"  Dodgson Done Right," and "Borda Done Right."  Of these three "done right" methods, only the latter fails the Condorcet Criterion.
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>Forest
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