[EM] Fwd: Two MMV definiions (brief, and ordered-procedure)

[Michael Ossipoff]

Anders:

You wrote:

[quote]
However, there’s no way to add another ballot to make B the unique winner,
in violation of resolvability.

This failure is silly because, if the three 4/3 defeats had been sorted in
_any_ strict order, D > A would have been ignored for already forming a
cycle with the 5/2 defeats, and the final result would unambiguously be A
> B > C > D.
[/quote]

In MMV as defined by me, both the DA and AB defeats are discarded
because they cycle with a set of defeats that contains stronger
defeats, but no weaker ones. That's a briefer wording of the
requirement in my definitions.

But, with DA and AB discarded, neither A nor B has a kept defeat, and
so the result is a tie bettween A and B.

The method against which your example is intended, in your initial
post, is different from MMT, and so I don't now if MMT even fails
Resolvability.   But, as I said, you'd have to say why Resolvability
is necessary.


[quote]
This feels like an oversight in the MMV definition, and although it’s
highly unlikely to matter in practice, fixing it is simple enough. At
each step, when considering a set of equally strong defeats, we should
immediately discard any defeats that would complete a cycle with strictly
stronger affirmed defeats, so that they are not considered for use in
cycles with equally strong defeats.
[/quote]

I'd said:

A defeat contradicts a set of other defeats if it is in a cycle
consisting only of itself and them.

Keep a defeat if it doesn't contradict a set of kept stronger kept
defeats, or a set consisting of defeats equal to it, and of kept
defeats stronger than it is.

[end of brief MMT definition]

Doesn't that do what you suggested?

But it returns a tie in your Resolvability example, when it declines
to keep DA and AB, resulting in A and B nether having a defeat.

Michael Ossipoff














On Sun, Dec 8, 2013 at 7:54 PM, Anders Kaseorg <andersk at mit.edu> wrote:
> On 12/08/2013 06:42 PM, Michael Ossipoff wrote:
>>
>> Brief definition:
>>
>> Keep every defeat that doesn't contradict a set of kept stronger defeats,
>> or a set consisting of defeats equal to it, and kept defeats stronger than
>> it.
>> [end of brief MMV definition]
>>
>> Ordered-Procedure MMV definition:
>>
>> In order of stronger first, consider the defeats one at time, as follows:
>> Keep the considerred defeat if it doesn't contradict a set of stronger
>> kept defeats, or a set consisting of defeats equal to it, and kept defeats
>> stronger than it is.
>> [end of ordered-procedure MMV definition]
>
>
> This still doesn’t fix the problem I pointed out yesterday[1].  Are you
> intending to fix it, or have you decided to fail resolvability in favor of
> making the definition shorter?
>
> Anders
>
> [1]
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2013-December/032423.html
>