[EM] Smith, Ext-Minmax(margins) appears to (third post, sorry)

[Kevin Venzke]

Hi,

Sorry for the third post in a row. I just realized that the original
scenario works whether you use Smith//MM or Smith,MM, it's just that
the winner is not C but D:

--- En date de : Sam 26.6.10, Kevin Venzke <stepjak at yahoo.fr> a écrit :
> What do you make of this scenario:
> 
> There are four candidates, ABCD. There is a cycle
> A>B>C>A. D is the
> Condorcet loser. The margins among A>B>C>A are 25,
> 30, 20, so that A has
> the weakest defeat among the Smith set. D's loss margins
> are 3 to A, 4
> to B, 5 to C.
> 
> Add 6 A>D ballots. Now D is in the Smith set and C's
> worst loss is only
> 1 vote, which is strictly the weakest, so the new ballots
> change the
> winner from A to C.

C's worst loss is still 30. A's worst is 14, B's 31.

D's worst loss is 9 votes, which is strictly the weakest, so D wins.
Whether D and his contests were excluded previously is irrelevant because
none of them were wins (this is margins, not PO), and even if they were,
they were all weaker than the other contests.

Kevin