[EM] Fwd: MMV and resolvability

[Michael Ossipoff]

 Alright, MMV/DED does have a problem. Looking again at my own
ordered-procedure defnition of MMV, I noticed that it isn't really
different from Prabhakar's definition, and that both definitions have
a seemingly-unavoidable problem of keeping a weaker definition, while
discarding stronger ones, for no reason other than that the weaker
definition is weaker. I agree that that's an unacceptable property.

When I first proposed DED/MMV to Steve Eppley, he told me that he'd
considered it, years before, and rejected it. That was a long time
ago, and Eppley didn't remember why he rejected it. I hoped that it
wasn't anything reallly bad. But, if MMV/DED's keeping of a weaker
defeat, while rejecting stronger defeats, for no reason other than
because it's weaker, is unavoidable, than I'd have to agree with
Eppley's rejection of that method.

Then, for dealing with equal defeats, that leaves Eppley's MAM, and
the Condorcet Internet Voting Service's version of Ranked-Pairs,
CIVS-RP.

CIVS-RP _keeps_, a set of equal defeats that are in a cycle that
doens't incude stronger defeats.

That avoids the problem that we've been speaking of, but Steve pointed
out that it can fail to deterministically disqualify a candidate who
should be deterministically disqualified, and which MAM would
deterministically disqualify. Steve sent an example of that to me.

So the advantage of MAM becomes clearer, when other equal-defeats
solutions are closely examined. But, when mid-count randomization is
unavailable or unacceptable, and tied outcomes are acceptable (maybe
to be solved by a randomizing method (that's more feasibly trustworthy
than mid-count randomization) ), then that suggests either DED/MMV, or
CIVS-RP.

Given the problem that Marcus has pointed out for MMV/DED, maybe,
then, under the conditions described in the previous paragraph,
CIVS-RP would be the way to go, in spite of the disadvantage that
Steve described.

Now, maybe DED/MMV can be fixed, and I just haven't noticed the fix. I
shouldn't say for sure. But, at the moment, it appears to me that,
because even my ordered-procedure definition doesn't avoid the
problem, I'm not finding a fix, and, at least right now, the problem
seems iherent in DED/MMV.

In any case, as a practical matter, at CIVS, we all completely trust
the mid-count randomization that is done at CIVS, and so there is no
reason to not use MAM at CIVS. MAM is the rank-count that I designated
as official, for my most recent poll at CIVS, my Internatonal
14-Party-Category poll.

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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