[EM] Fwd: MMV and resolvability

[Michael Ossipoff]

 Two things:

1. Another typo:

In my post just before this one, I said "mid-vote randomization", when
I meant "mid-count randomization".

2. It isn't just by my own wording, that MMV doesn't have the probem
that you (Anders Kaseorg) described. Prabhakar's wording, it seems to
me, doesn't have that problem either. Here is what Prabhakar said:

[quote]
 (i) If a matchup later in the list conflicts with the
previously-determined order, the latter matchup is superseded
(ignored).

(ii) In the even unlikelier case where several matchups with same-size
majorities conflict with each other, all such conflicting matchups are
ignored (though any non-conflicting matchups of that size are still
included).
 [/quote]

According to (i), your D>A defea is ignored in MMV, because it
conflicts with the previously-determined order.

Paragraph (ii) isn't needed to disqualify D>A, because D>A is
disqualified before we get to (ii). D>A is disqualified by (i).

Paragraph (ii) speaks of disqualifications too, but it doesn't say
anything about un-disqualifying defeats that are disqualifed under
(i).

So, Prabhakar's wording disqualifies D>A, in your example.

Of course it's useful to specify a procedure, but i like my brief MMV
definition:

Keep every defeat that doesn't contradict a set of kept stronger
defeats (by being in a cycle with them)..

[end of my brief MMV definition]

Of course it goes without saying that keeping a defeat means
disqualifying the candidate defeated in that defeat. A defeat is a
public pairwise decision that says Y shouldn't win because X is better
than Y.

As I said, my wording, above, when applied literally, amounts to MMV.

Michael Ossipoff





On Sat, Dec 7, 2013 at 6:34 AM, Anders Kaseorg <andersk at mit.edu> wrote:
> Maximum Majority Voting exhibits a silly failure of Tideman’s
> resolvability criterion in the following four-candidate election:
>   3: A > B > C > D
>   1: B > D > A > C
>   2: C > D > B > A
>   1: D > A > B > C
>
> According to my reading of
> http://radicalcentrism.org/resources/maximum-majority-voting/, and also
> according to Eric Gorr’s calculator at http://condorcet.ericgorr.net/, MMV
> proceeds as follows.  The defeats are sorted:
>   5/2: A > C, B > C, C > D
>   4/3: A > B, B > D, D > A
> In the first step, MMV affirms the three 5/2 defeats.  In the second step,
> it ignores all three 4/3 defeats because they form a cycle.  The final
> result is A = B > C > D.
>
> 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.
>
> 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.
>
> Anders