# [EM] Cloneproof SSD

MIKE OSSIPOFF nkklrp at hotmail.com
Tue Jan 16 17:37:36 PST 2001

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Blake wrote:

>I consider Beatpath winner to be slightly simpler than SSD.  What is
>SSD's obvious motivation?

If we have a set of candidates none of whom are beaten by anyone outside
the set, then those candidates are obviously more qualified to win.

Condorcet suggested his procedure because the propositions (pairwise
defeats) cannot all exist together. The ones that cannot all exist
together are the ones among the current Schwartz set. The defeats by
Schwartz set candidates against non-Schwartz-set candidates are
not contradicted by any other defeats. The only defeats that are
contradicted, for the purpose of choosing a winner, are those among
the current Schwartz set.

The people are saying  that the Schwartz set candidates are the
ones that aren't bested by anyone. So it's intuitively natural &
obvious to only drop defeats from among the current Schwartz set.

And the idea of dropping defeats is itself natural too. We don't have
a winner because everyone has a defeat. That means that, no matter whom
we elect, we have to overrule a pairwise defeat, disregard it. And so
doesn't it make sense to overrule a weak defeat, since we have to
overrule a defeat?

So it seems to me that everything about SSD is natural & obvious.

As I've said, I explained SSD to someone who had no prior exposure to
voting systems. I used a diagram that I drew while I spoke. She understood
it perfectly, and agreed that the candidates in the innermost
unbeaten set are the ones who qualify to have a defeat dropped, because
the voters have said that they aren't bested by anyone outside that
set.

But try telling someone about a method based on beatpaths. It will
seem arbitrary to them. Why that instead of some other rule?
Sure, you could say that a beatpath is an indirect defeat by which
the people are saying that A is better than C, when A>B>C.
And if C has a similar relation to A, via C>D>A, then it's reasonable
to ask which of these indirect statements is stronger. But then
there's the question of how to measure a beatpath's strength.
Someone could point out that a "weakest link" analogy with a chain
isn't really valid. The chain breaks only at one link, the weakest one.
But the pairwise defeats all exist at the same time, and the overall
validity of a beatpath appears to be dependent on the strength of all
of its defeats.

So, overall, the beatpath approach will sound arbitrary. The
Schwartz set approach sounds completely obvious & compelling.

Have you defined BeatpathWinner to someone with no prior exposure to
voting systems? Try it, and tell me how clear its motivation is to
them.

Mike Ossipoff

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