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

[Juho Laatu]

One more observation on clones. I think there is a major difference between methods that systematically favour or disfavour groupings with multiple candidates (e.g. Borda where nomination of two candidates instead of one typically changes the results dramatically) and methods that can break the clone criterion in some exceptional situations. For example minmax can handle clones perfectly well if we study only those cases that do not have any loops. If we assume that loops are rare, or that they are weak if they happen to exist, also then there are no significant risks (nor benefits) if some groupings do nominate multiple candidates. I guess it is quite correct to say that in typical elections (where large number of voters make independet decisions) Borda has practical problems with clones, while minmax doesn't (although both formally violate the EM clone criterion). That difference is important when one looks for practical election methods (i.e. not just study theoretical properties of different methos / compliance with various formal criteria).

Juho


On 05 Nov 2014, at 22:54, Toby Pereira <tdp201b at yahoo.co.uk> wrote:

> 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)
> 
> Toby,
> 
> 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..
> 
> 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. 
> 
> 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.
> 
> Forest
> 
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> 
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> 
> 
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