[EM] Condorcet cyclic drop rule

[Blake Cretney]

On Thu, 05 Apr 2001 03:06:57 -0000
"MIKE OSSIPOFF" <nkklrp at hotmail.com> wrote:

> 
> > > the MinMax interpretation of Condorcet's wordings has been
> > > proposed by Black (Duncan Black, "The Theory of Committees
> > > and Elections," Cambridge University Press, 1958).
> >
> >Is that really an interpretation, or a new method based on
Condorcet's
> >principles?
> 
> If you're talking about what you call "Minmax", it's an
interpretation
> of Condorcet's drop-weakest definition. The way I currently define
> PC is the literal interpretation of Condorcet's drop-weakest
proposal.
> Yes, if he was interested in dropping the proposition least likely]
> to be "correct", then that suggests margins, 

But my case is much stronger than that.  I've been saying all along
that Condorcet must have meant margins because of his probability
concern.  You never acknowledged the slightest possibility.  What's
changed now is that I've shown an example that proves that Condorcet
used the word plurality as I had claimed.  So there can't be any
doubt.  Its absurd for you now to say that his probability concerns
"suggest margins" as if that was my whole case, especially since when
that was my whole case, you didn't give it any credibility.

> but the literal wording of his proposal suggest defeat-support. 

The only reason the "literal wording" suggests defeat-support to you
is that you define plurality and majority differently than did
Condorcet.

> >Note that originally Mike called this "Condorcet's Method", and
some
> >people, like Rob Lanphier, still do.
> 
> Others call it Condorcet's method. That name is found for it in
> journal articles, though we don't know how those articles would
> measure defeats, with incomplete rankings. It especially deserves
> the name Condorcet's method, since it's the literal interpretation.

If these articles attribute it to Condorcet, then I think they have
misinterpreted him, unless they are referring to quotes I haven't
seen.  I'd appreciate it if someone could quote one of those articles,
though.

> >Iain Mclean, Fiona Hewitt, 1994
> >"Condorcet:  Foundations of Social Choice and Political Theory"
> >Edward Elgar Publishing Limited
> >
> >p 238 (of the translation) from "On Elections" 1793
> > > A table of majority judgements between the candidates taken
> > > two by two would then be formed and the result -- the order
> > > of merit in which they are placed by the majority --
> > > extracted from it.  If these judgements could not all exist
> > > together, then those with the smallest majority would be
> > > rejected.
--snip--
> You seem to think that Condorcet wanted to eliminate all cycles.
> But he said to elect the voted CW. If he wanted to get rid of all
> cycles, then he wouldn't have just said to elect the voted CW.

Well, I advocate a method that gets rid of all cycles, and I also say
to elect the CW.  The crucial point is that getting rid of the cycles
can't change the CW.  You act as if advocating the CW and getting rid
of all cycles are mutually exclusive goals.

> What caused him to say that the propositions cannot all exist
together

He says that they "could not" all exist together.  Your mistake is
telling, because your interpretation would be less unnatural if he had
worded it like that.

> is if there's no voted CW, eveyone has a defeat. Since that's the
> only reason why he's dropping defeats, then we stop dropping them
> as soon as someone's unbeaten.

So, your point of view is that when Condorcet says that the
propositions couldn't all exist together, he means that they couldn't
all exist together because then everyone is defeated, and this
frustrates the goal of electing a winner.

I think that he means that they couldn't all exist together, because
they are inconsistent, and couldn't all be held by a rational mind. 
The word "couldn't" implies that he is comparing the actual situation
to a hypothetical one (such as these judgements all existing in a
ration mind).  

> A table of majority judgements between the candidates 
> taken two by two would then be formed and the result -- 
> the order of merit in which they are placed by the 
> majority -- extracted from it.

Note that he does not say, "the unbeaten candidate will be extracted
from it."  He says, "the order of merit."  So, don't we have to
conclude that that is the goal of his procedure?  Contrast what he
actually said with your characterization:

> But he said to elect the voted CW. If he wanted to get rid of all
> cycles, then he wouldn't have just said to elect the voted CW.

Furthermore, its natural to think that contradictory judgements could
not, in some sense, exist.  But why would Condorcet say that
judgements couldn't exist, simply because they don't provide an
unbeaten candidate.

Anyway, here's an earlier statement in the same essay:

p236
> When a man compares two individuals and prefers the 
> second to the first, and then, on comparing the second 
> with a third, prefers the latter, it would be 
> self-contradictory if he did not also prefer the third to the 
> first.  If, however, on making a direct comparison of the 
> first and the third, he found reasons for preferring the 
> first, he would then have to examine this judgement, 
> balance the reasons behind it with those behind his other 
> judgements (which cannot exist alongside this new one) 
> and sacrifice the one he considers least probable.

Let me make a few points:
- Condorcet never says that any of these three candidates are the
man's favourite.
- The problem he states is that the man's opinions are originally
self-contradictory (not that they prevent him from choosing a
favourite).
- He uses the phrase, "cannot exist" to describe this situation.  That
is contradictions cannot exist in a rational mind (at least if they
are examined).

If you read further it is clear that Condorcet draws an analogy
between this rational man, and his way of  considering the votes. 
Then, in describing his method, he says, "If these judgements could
not all exist together..."

When Condorcet says this, he has already established what it means for
judgements not to be able to exist together.  They contradict.  The
"could not" implies a different situation.  What fits is the situation
he has already described of a rational man. 

> Again, his top-down proposal does imply getting rid of all cycles,
> and was reasonably interpreted by Tideman as what
> Tideman called Ranked Pairs.

I might be wrong, but in what I've read, Tideman didn't claim to be
interpreting Condorcet.  He may feel his method is in line with
Condorcet's principles.  There's a difference.

---
Blake Cretney