[EM] Cloneproof SSD

[Blake Cretney]

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

First, let me admit that I see SSD (winning-votes) as consistent with
your general views.  However, since you asked, I'll explain how I see
the matter.

First, it's worth considering why we might not want to drop (or skip)
victories.  One explanation is that these represent majority opinions,
and that the majority has a right to get its way.  Whether or not we
agree with the principle, I think this view is a misunderstanding.  Even
in a simple example,

40 A B C
35 B C A
25 C A B

A>B 65-40
B>C 75-25
C>A 60-40

We'd both agree that A wins.  In trying to explain why C loses, it is
tempting to claim that a majority voted B over C, and that this majority
has a right to get its way.  The problem is that the people who voted B
over C don't all prefer A to C.  In fact, not enough do to give A a
majority over C.  So, if we are upholding the A over C majority's
rights, we are doing it over the clearly expressed wishes of many of
them.  To me, that sounds like nonsense.

Instead, I view the ballots as evidence.  It isn't a question of rights.
 It is a question of which candidate comes out looking best based on the
evidence provided by the ballots, and in particular, by the pairwise
contests.

Now, when there's a Condorcet winner, that's like an open and shut case.
 All the evidence is pointing in one direction.  However, when there's a
cycle, like up above, the evidence is somewhat contradictory.  So, what
you do is what you would do if you were investigating a crime.  You come
up with multiple internally consistent theories, and see which is best
supported, or least contradicted, by the evidence.

I expect that majorities will be correct more often than if they made
decisions by pure chance.  So, a theory that goes against a majority
decision has disconfirming evidence to deal with.  The stronger the
margin of the majority, the stronger the evidence.  That's why I don't
like to drop or skip majorities.

Now, recall that I said that you would consider internally consistent
theories.  In an election, A>B>C>D is an internally consistent theory
about the candidates (consider > to mean is better than).

D>A,B,C and A>B and B>C and C>A

Is a theory that is not internally consistent.  It can't be true that
B>C>D>B.  So, no matter how well that fits the external evidence, it
can't be true.  You wouldn't even consider it.

I see this as the chief difference between Ranked Pairs and SSD. 
Consider the following example (> means pairwise beats).

A>B 40
B>C 39
C>A 38
A>D 8
D>B 9
D>C 10

Ranked Pairs chooses A.  In fact, it chooses the complete ranking
A>D>B>C.  To do this, it has to skip/drop C>A 38.  This ranking is
consistent with all other victories.

SSD isn't defined to give a complete ranking.  It drops A>D 8, then it
eliminates the other candidates besides D.  Now, if you claim that only
A>D 8 is over-ruled, this makes good sense.  The cycle A>B>C>A hasn't
been resolved, so you haven't had to drop any of these victories.  But
we know that these victories can't all be true.  It is only because SSD
doesn't try to form an internally consistent theory that this is
permitted.  By rights, since one of A>B>C>A must be false, Ranked Pairs
shouldn't be criticized for dropping one.

But if one of these must be dropped, then why drop the A>D victory too? 
What is gained?  It appears that this victory is dropped only because it
was necessary to drop a victory for the SSD procedure to continue.

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