# [EM] MMV and resolvability

Michael Ossipoff email9648742 at gmail.com
Mon Dec 9 06:37:13 PST 2013

``` Regarding Markus' two nonmonotonicity examples:

With Fixed MMV, by my brief definition (the one that doesn't
explicitly state an ordered procedure), either in my most
recently-posted 1-stage version, or Anders' 2-stage version, or in the
3-stage version that I suggested a few minutes ago, Markus' example
doesn't have the nonmonotonicity that he described for a different MMV
version.  The problem of a weaker defeat being kept, when stronger
defeats are rejected, for no reason other than that weaker defeat is
weaker, doesn't happen with the 3 improved MMV versions that I named
in this paragraph.

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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