[EM] Cloneproof SSD

[Blake Cretney]

"MIKE " <nkklrp at hotmail.com>, on the subject of 'Re: [EM] Cloneproof
SSD', is quoted a

>>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.

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.

>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.

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.

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

>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.

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

The answer, it seems to me, is that we can't take these victories as
independent assessments.  After all, they are made by the same people,
likely on many of the same grounds.  

I haven't field tested either explanation, though.

---
Blake Cretney
See my Ranked Pairs site at
http://www.fortunecity.com/meltingpot/harrow/124/path