[EM] Cloneproof SSD

[MIKE OSSIPOFF]

Blake wrote:

>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,

Though the majority defensive strategy criteria are about what a
majority shouldn't have to do to get its way, the motivation for
dropping the weakest defeat doesn't come from criteria and doesn't
involve the word "majority". We drop the weakest defeat because
no matter whom we elect, we're going to have to disregard & overrule
a pairwise defeat. Say A beats B beats C beats A. If we elect A,
then we're ignoring the people who voted C over A and made C beat A.
They won that pairwise victory, and we're overruling it, and them.

That shouldn't be done lightly, and so, if we must overrule a defeat,
let's overrule the one that has fewest people voting for it.

But, as I said, the only defeats that are in mutual conflict, for choosing a 
winner are the defeats among the Schwartz set. Hence SSD.

>
>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.

I don't use majority to explain why C doesn't win. I merely point out
that, by dropping A>D, and electing D, we overrule fewest voters.

>
>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.

I claim that rights are more important. The voter's right to not be
overruled. If we must overrule someone, then let's overrule the fewest
possible.

I'm just talking now about motivation for SSD. Of course the criterion
compliances are the really important reason for liking a voting
system.


>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.

But since we're only required to choose one winner, we don't need
a theory about the relative merits of all the candidates. If there's
such a thing as absolute merit, then the people are wrong about one
of the defeats in A>B>C>A, but that fact that they're wrong about
one of those needn't concern us. A>D is supported be the fewest
people. And if we don't count A>D, then we can elect D. (...in Blake's
examlple below)

>
>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.

I understand the case that you make, and if a completely consistent
theory about the pairwise relative merit of all the candidates is
considered an important standard, then that counts in Tideman's favor.

It's just a question of different standards. I'd rather overrule fewer
voters. I'm more interested in voters' right to not be overruled than
in a consistent theory about pairwise relative merits of all the
candidates.

Now, someone could say "Then, instead of dropping weakest defeats 1 by
1, why don't you elect the candidate who, when we sum the votes
in favor of all his defeats, has the lowest sum?". Ok, that would
_really_ minimize overuling of voters. But I don't know if it would
have the criterion compliances that I & some others want. Of course
that's worth checking out. Would that method defined in this paragraph
meet the majority defensive strategy criteria? Would it meet ICC in
small committee elections?

I wouldn't consider proposing this "Minimize Overruling" method
for public elections unless it did as well as SSD in those elections.
I wouldn't propose it for small committees unless it did as well
as Cloneproof SSD in those elections. I'm talking about criterion
compliances.

Mike Ossipoff
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