[EM] MAM vs Schulze

[Michael Ossipoff]

(Replying farther down)

On Oct 9, 2016 1:02 AM, "Markus Schulze" <markus.schulze at alumni.tu-berlin.de>
wrote:
>
> Hallo,
>
>
> > MAM doesn't disregard a defeat unnecessarily or without
> > obvious, compelling justification.
>
> 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..

(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



> Markus Schulze
>
>
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