[EM] Cloneproof SSD

[MIKE OSSIPOFF]

>"MIKE " <nkklrp at hotmail.com>, on the subject of 'Re: [EM] Cloneproof
>SSD', is quoted as saying:
>
> >>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.
>
>What you're saying is that you might have two candidates A and B that
>are pairwise tied, and a third candidate C, where A beats C and C beats
>B.  So, A should beat B.  Now, that might be true, but since your basing
>the A over B victory on a third alternative, it appears to me that the
>result is rather counter-intuitive, instead of obvious.  I think most
>people intuitively agree with Arrow that candidates like C should be
>irrelevant.

Right, and the fact that B ties with A means that the people have
said that B is as good as A. So I'm not saying that it's really wrong
to violate the Schwartz Criterion. But my point is that neither is
it objectionable to not violate it, to choose from within the Schwartz
set. As I told Markus, it's even rather un-aesthetic to choose outside
of the Schwartz Set. So my point is just that no one can object that
it doesn't make sense to say that the candidates in the Schwartz set
are special, and that their defeats of other candidates are unconflicted
& uncancelled & unopposed by other defeats.


>
>You have to be careful not to imagine the Schwartz set as a team.
>They're not all on the same side, and do not necessarily want to help
>each other out.

Fair enough. I didn't mean to imply anything like that.

>
> >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?
>
>Here's my problem with that.  I agree that we have to drop defeats.  I
>also agree that we should not drop defeats unnecessarily.  However, the
>process of iterating Schwartz imposes some requirements.  We often have
>to drop defeats just to keep the process going.  So, we might have to
>drop defeats that would be unnecessary to drop if we only wanted to
>impose consistency.

Aren't all the defeats among the Schwartz set mutually inconsistent
for the purpose of calling someone a winner?

>
>It's a similar problem to IRV.  Obviously some candidates are going to
>be dropped (in the sense that not all candidates can win).  It's also
>obvious that if you only look at first place votes among non-dropped
>candidates, that IRV picks the right candidate to drop.  However, if we
>don't assume these restrictions, it isn't clear that IRV is dropping the
>right candidates.

But what restrictions does SSD have? Dropping the weakest defeat
among the Schwartz set may be a restriction, but what's wrong with it?
Is there a sense in which it doesn't make sense or have justification?
What would be an example in which it would? An example in which
doing so would drop a defeat that doesn't need to be dropped for
consistency?


>
>Now, you could argue that both IRV and SSD are natural and obvious, in
>that most people wouldn't see this problem

I admit that many people consider IRV obvious & natural, and
I'm not saying it isn't. But its justification, though obvious &
natural to many, is criticizable. I have yet to hear a _specific_
criticism of SSD's obvious & natural justification & motivation.
With an example.

[referring to the "weakest link" analogy]:

>I think that the analogy fits perfectly.  A "beatpath" really is
>dependent on the strength of its weakest victory.

Suppose a beatpath contain 2 adjacent defeats: 53 to 47, and
52 to 48. The latter is the weakest. The validity of the conclusion
that, by the beatpath, the people are saying that the candidate at
one end of it is better than the candidate at the other end of it--
the validity of that conclusion depends on each link. To the extent
that either of the abovenamed defeats is weak or questionable, it
puts the whole thing into question. The 52 defeat is weaker, but
surely the 53 defeat, being about the same, hurts the validity of
the conclusion by about the same amount.



>That doesn't explain
>why this method is used, though.  The answer would be very similar to
>the answer you would have to give if someone asked you why in SSD, one
>large victory can over-rule several victories that are almost as large.

I'd just suggest that the questioner look at it one step at a time.
"Which is the weakest defeat among the Schwartz set right now?"

There's a case for arguing for method that seeks to literally minimize
the overruling of voters. It might have better SU under sincere voting.
It probably would sacrifice strategy criteria compliances though.
But let's find out.

>I haven't field tested either explanation, though.

I know that one of them works.


Mike Ossipoff

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