Hallo,

It is not a characteristic property of MAM that it "doesn't
disregard a defeat unnecessarily or without obvious,
compelling justification". Many methods can be described in
this manner: MAM, Schulze, River, MinMax, Kemeny-Young, etc..

Markus Schulze

(Replying farther down)

On Oct 9, 2016 1:02 AM, "Markus Schulze" markus.schulze@alumni.tu-berlin.de
wrote:

(endquote)

Yes, I suppose that anything could be called " obvious, compelling
justification ". So that wording of mine was unhelpful.

My comparison was intended for pure pairwise-count methods that choose a
winner based on pairwise defeats.

Sometimes there's a cycle, and therefore no immediately obvious winner. To
declare a winner amounts to disregarding hir defeat(s).

We want to disregard as few defeats as possible. Plainly, if it's necessary
to disregard one of the defeats in a cycle, then it should be the weakest
one.

When CSSD starts dropping defeats, the weakest defeat in the current
Schwartz set, a stronger defeat that makes it the weakest, might, itself,
be similarly contradicted, overruled & nullified.

If a defeat is nullified, overruled, contradicted, by being the weakest in
a cycle with stronger un-nullified defeats, then is it really necessary to
drop a defeat that it cyclically contradicts?

That's a big flaw in CSSD's justification.

And it's why, when MAM & Schulze choose differently, the MAM winner is
usually publicly preferred to the Schulze winner.

MAM:

A defeat is affirmed if it isn't the weakest defeat in a cycle whose other
defeats are affirmed.

(end of definition)

There's no mention of an order of operations.

We don't drop, invalidate or disqualify a defeat because it's cyclically
contradicted by defeats that, themselves, are cyclically contradicted by
qualified, valid stronger defeats.

No, there's no circularity there, just recursion.

If we want to disregard a defeat only if necessary, only if it's overruled
by being weakest in a cycle with un-overruled defeats, then MAM is the one
& only method that achieves that (because that's literally what MAM's
definition says).

If the need to disregard a defeat is due to its being cyclically
contradicted by stronger defeats that can't be thus disregarded, then MAM
is the only method that doesn't unnecessarily disregard defeats.

Therefore it's no surprise that the MAM winner is usually publicly
preferred to the Schulze winner.

Michael Ossipoff e

I almost agree with that but not quite. When picking the winner, the target is not to make the group opinion a linear opinion (where cycles have been broken, and some pairwise defeats disregarded). The idea is rather to accept the fact that group opinions may sometimes be cyclic, and identify a single best winner despite of that. One needs to identify one winner, but there is no need to break cycles of make the group opinion linear.

It is a fact that if there is no Condorcet winner, there is some candidate that would beat the winner in a pairwise comparison. But that's about as far as we need to go in the direction of disregarding defeats.

Some methods may well be based on a philosophy that is based on breaking cycles, but others need not do that. One simple example could be one that resorts to Approval if there is no Condorcet winner. That method quite clearly makes some sense, but doesn't break any cycles, or at least doesn't care about the preference strengths of the cycles, or the pairwise losses of the winner.

Just trying to be very exact on what the single winner methods are supposed to do.
BR, Juho

If course breaking cycles isn't the only approach to finding the right
winner. But it's the basis of MAM & CSSD, &, in general, the methods that
look only at pairwise defeats, & disregard defeats to make someone
unbeaten..

So I brought it up in connection with the comparison between MAM & Beatpath.

Cycle-breaking methods aren't among my favorite proposals.

3-Slot ICT
Approval
Score
Plain MMPO
Bucklin

Michael Ossipoff
On Oct 9, 2016 12:56 PM, "Juho Laatu" juho.laatu@gmail.com wrote:

Ok, accepted. :-) Except that some methods like minmax look at pairwise defeats, but do not aim at breaking cycles (and forcing out a linear preference order). :-) Maybe at least all "path based" methods aim at breaking cycles. (All methods of course ignore at least one defeat if there is no Condorcet winner.)

BR, Juho