[EM] MMV and resolvability
Michael Ossipoff
email9648742 at gmail.com
Sun Dec 8 13:22:54 PST 2013
The only thing wrong with my ordered-procedure MMV definition was
that I left something out:
MMV (ordered-procedure definition):
A defeat contradicts a set of other defeats if it is in a cycle
consisting of only it and them.
In order of stronger first, consider each defeat as follows:
Keep it unless it contradicts a set of stonger defeats, or a set
consisting of defeats equal to it and defeats stronger than it.
[end of ordered-procedure MMV definition]
Of course an alternative wins if it doesn't have a kept defeat. If
there are more than one winner, and if it is desired to choose just
one alternative, then random-ballot should be used for choosing among
the winners.
By the way, my brief definition doesn't do wrong in Marcus' examples.
It merely doesn;t give any result. "No result" can be construed as a
tie.
Michael Ossipoff
On Sun, Dec 8, 2013 at 12:05 AM, Markus Schulze
<markus.schulze at alumni.tu-berlin.de> wrote:
> Hallo,
>
> here is another example to illustrate MMV's violation
> of monotonicity.
>
> Situation 1:
>
> A>B, B>C, C>D, D>A, D>E, E>A each have the same
> strength and are stronger than every other pairwise
> defeat.
>
> The other pairwise defeats are (sorted by their strength
> in a decreasing order):
>
> A>C
>
> C>E
>
> E>B
>
> B>D
>
> MMV skips A>B, B>C, C>D, D>A, D>E, and E>A, since they
> form a directed cycle.
>
> Then it locks A>C,C>E,E>B, and B>D, so that A is the
> unique winner.
>
> Situation 2:
>
> Some voters rank candidate A higher (relatively to
> candidate D), so that the pairwise defeat D>A becomes
> weaker.
>
> A>B, B>C, C>D, D>E, E>A each have the same
> strength and are stronger than every other pairwise
> defeat.
>
> The other pairwise defeats are (sorted by their strength
> in a decreasing order):
>
> A>C
>
> C>E
>
> E>B
>
> D>A
>
> B>D
>
> MMV skips A>B, B>C, C>D, D>E, and E>A, since they
> form a directed cycle.
>
> Then it locks A>C,C>E,E>B, and D>A, so that D is the
> unique winner.
>
> Thus, by ranking candidate A higher candidate A is changed
> from a winner to a loser.
>
>
> Markus Schulze
>
> ----
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