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

[Michael Ossipoff]

Fixed MMT:

To keep a defeat is to disqualify its defeated alternative from winning.

A defeat contradicts a set of defeats if it's in a cycle consisting
only of it and that set of defeats.

Keep every defeat that doesn't contradict a set of kept stronger defeats.

Then, among the kept defeats, un-keep each defeat that contradicts a
set consisting of defeats equal to it, and of kept defeats stronger
than it is.

[end of fixed MMT definition]

Or maybe word it in terms of discarding instead of keeping:

Discard every defeat that contradicts a set of un-discarded stronger defeats.

Then discard every defeat that contradicts a set consisting of defeats
equal to it, and of un-discarded defeats stronger than it it is.

[end of discard-worded fixed MMT definition]

Maybe there should be a 3rd stage that discards any set of equal
defeats that contradict only eachother. Discarding such a set is
problematic in the unfixed 1-stage version, because it can keep a
weaker defeat, while discarding stronger ones, for no reason other
than that the weaker one i weaker. Maybe that problem and objection
wouldn't apply in the fixed version, if that 3rd stage were added.

Ok, your fix for MMV doesn't guarantee Resolvability. I never
understood the need for Resolvabiliy anyway. After I posted last
night, I realized that I'd been exaggerating the importance of
brevity. At EM, we've usually been discussing what would be good for
U.S. elections, right now. Current conditions. Because of chicken
dilemma and media-deception-induced favorite-burial need, I don't
recommend ideal majoritarian methods for current conditions. And,
because of chicken dilemma, I don't recommend ideal majoritarian
methods for the Green scenario either. Polling experience suggests
that ideal majoritarian methods are the best choice for polling,
because the absence of top-cycles in polling-results shows that
succesful chicken-dilemma defection isn't happening in polls.

So, anyway, my emphasis on brevity was due to how great an advantage
RP's brevity would be for offering it to the public, for official
public elections. But, since I don't recommend such a method for
official public elections in the U.S. right now (I recommend Woodall
and Benham instead, to avoid chicken dilemma), brevity isn't really so
important.

I'm not saying that definition-brevity has no importance, but it's a
lot less necessary for polling, and for organizations. A lot fewer
people need to be convinced about the method, and they're people who
are more interested, too. That's dramatically demonstrated by the
great popularity, for organizations, of Beatpath, whose definition is
considerably less brief than that of Ranked-Pairs (RP).

And, Resolvability aside, the fix that you suggested makes perfect
sense, just as a matter of rightness. In your example, DA is different
from AB and  BD, because DA contradicts a set of defeats that are
stronger than it is. DA is fully-qualified for rejection, by the
accepted Ranked-Pairs standard. The need to randomly choose, or
simultaneouslly keep or reject, doesn't really apply to {AB, BD, DA}.
Of course the most right thing do do, there, is to first reject DA.

Then, as you said, AB is kept, and A is the unique winner.

What should that fixed method be called? Fixed MMT, Improved MMT?

Actually, it doesn't even lose much brevity, because the same wording
is still needed either way, though the fixed method divides it into
two statements.

Michael Ossipoff



On Mon, Dec 9, 2013 at 4:09 AM, Anders Kaseorg <andersk at mit.edu> wrote:
> On 12/08/2013 10:11 PM, Michael Ossipoff wrote:
>>
>> Ok, you mean, when some equal defeats would otherwise all get
>> simultaneously discarded because they cycle with eachother and some
>> stronmger defeats, we should give first priority to first discarding
>> any of those equal defeats that are the only defeat of that strength
>> that is in some other particular cycle with defeats all of which are
>> stronger?
>
>
> Yes, that’s the difference.
>
> Since you named MMV, the choice of definition is up to you.  We just
> wouldn’t want the definition to have two interpretations under which it
> might be argued that the same election had two different results (A = B > C
>> D or A > B > C > D).
>
>
>> Sure, that sounds like it makes sense, and maybe it would be an
>> improvement.
>>
>> Does MMT as I define it fail Resolvability, and woud your fix make
>> it pass Resolvability?
>
>
> I’ve now done some more investigation and found that resolvability failures
> still exist with or without the fix.  For example,
>
> Ballots:
> 1: A > D > C > B
> 1: A > C > D > B
> 1: D > C > B > A
> 1: B > A > C > D
> 1: C > D > B > A
> Defeats:
> 4-1: C > B, D > B
> 3-2: A > C, A > D, B > A, C > D
> Result: C = D > B
>
> but there’s no extra vote that would break the tie in favor of D.  So
> perhaps the fix is not as helpful as I thought.
>
> Anders