[EM] monotonicity + clone independence = Condorcet?

[Kevin Venzke]

Hi Ross,

 :Ross Hyman <rahyman at sbcglobal.net>
À : "election-methods at electorama.com" <election-methods at electorama.com> 
Envoyé le : Vendredi 25 avril 2014 17h10
Objet : [EM] monotonicity + clone independence = Condorcet?
 

Conjecture:  If ballots rank all candidates with no equal ranking then any method that is both monotonic and independent of clones will elect the Condorcet winner if there is one.
>Can anyone supply a proof or provide a counter example showing it is not true?


Woodall made a few methods that violate Condorcet but satisfy Clone-Winner, Clone-Loser,
and Mono-Raise. They all use the "descending coalition" concept. The simplest one is Descending Solid 
Coalitions (DSC). He gives this example of Condorcet failure, which works for both DSC and DAC:

46 A>B>C
3 A>C>B
3 B>C>A
48 C>A>B

The CW is C, but in DSC and DAC the winner is A. What happens is that the ACB and CAB voters form
the largest coalition (for {A,C}), which disqualifies B from winning, but the 49 voters liking A best are 
stronger than the 48 voters that like C best, or alternatively the 3 voters that like A the least.

What he calls "Approval AV" (i.e. IRV eliminating based on the initial "votes in total" figure, which can't
change due to eliminations, selecting the winner once someone has a majority of the transferable votes) also
may count. (Depends on whether you say the cloning operation can cause a candidate on a ballot to split 
into candidates that are not uniformly either ranked or unranked just as the original candidate.)

I think Random Ballot might count depending on your definitions.

Kevin Venzke
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