[EM] Condorcet cyclic drop rule

[MIKE OSSIPOFF]

 > 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.

I should have acknowledged it if I didn't, because that was obvious to
me since the 1st time I read about Condorcet in Duncan Black's book,
a long time ago. I don't know why I didn't acknowledge it, but I
didn't deny that Condorcet's interest in probabilities suggests that
he'd have wanted to use margins.

I've been saying that his method wording says defeat-support, and
Norm's dictionary information confirmed that claim.

You posted that formula that explicitly shows margins, a formula
about probabilities. Sure, but the margins don't appear explicitly
in his method wordings. So, unless I've missed something in your
messages, I don't understand how that formula means that his method
wordings specify margins. Unless I've missed some translated quote
in your messages, from his method proposals, it still seems as if
Norman's dictionary information is all we have to go on about the
best guess on what his wording seems to say, according to the French
at Condorcet's time. Now, I agree that, because of his interest in
probability, he may well have intended margins. All I'm saying is that,
according to Norm's late 18th century French dictionary, his wording
itself--apart from other considerations--suggests defeat-support.
I don't deny that, based on his interest in the probability of
propositions being "correct", he probably intended margins.



>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

Well, it's your whole case unless you've posted _method definition
wording_ translation of Condorcet that specifies margins. But even
if it's your whole case, I don't deny that it's a convincing case.

I'm going to check the recent archives to find out if there's some
method definition quote that I missed, in which Condorcet explicitly
specifies margins _in a method definition_.


, especially since when
>that was my whole case, you didn't give it any credibility.

Maybe I didn't comment on the fact that his interest in probability
implies that he intended margins. I don't know why I didn't.
I wouldn't pretend to not know that for the sake of claiming that
defeat-support is the only Condorcet's method. I believed that
defeat-support is the only Condorcet's method, based on the actual
method wording. Inferring from the fact that he expressed the purpose
of estimating propositions' probability of being correct, that didn't
seem to me as compelling, for saying what "Condorcet's method" means,
as compared to actual method definition wording. Again, I don't know
why I believed that, because now it does seem that, due to Condorcet's
interest in probabilities, margins versions qualify as Condorcet's method.

I still think defeat-support qualifies too, due to the method wordings
written by Condorcet. Anyway, "Condorcet's method" is often used
way too broadly, to mean any "Condorcet completion method", any
pairwise-count method.

Anyway, I agree that that it didn't make sense to want to exclude
margins versions from being Condorcet's method--in view of Condorcet's
writing about probability. As I said, I don't know why I excluded margins
from my definition of Condorcet's method, knowing about Condorcet's
interest in probabilities, but I claim that I wouldn't try to sweep
the probability information under the rug in order to have a better case for 
saying that margins isn't Condorcet's method. That was just my
impression at the time, though apparently not a fair impression, and
maybe one influenced by unintentional bias against a defeat-measure
whose results I don't like.

>
> > 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.

...but not differently from the late 18th century French dictionary.
Sure, maybe the probability information, though external to his
method definitions, means that he meant those words the way you
claim.


>
> > >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.

The usual academic definition of Condorcet's method is: Elect the
candidate whose greatest defeat is the least. That's equivalent to:
If no one's undfeated, drop the weakest defeat, repeatedly till someone
is undefeated. That's how I interpreted the translation of Condorcet's 
words.

>
> > >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.

I just meant that the absense of a voted CW seems to be his reason
for dropping defeats. Once we get one undefeated candidate, the
situation that made the dropping necessary seems to be gone. At least
that was my impression of what sounded like his reason for dropping
defeats.

>
> > 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.

Yes, that's how I took it.

>
>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:

Ok, if you're saying that Condorcet said to drop the weakest defeat
till there are no cycles, doesn't that result in something similar to
DCD, and unlike any of our proposals? It certainly isn't Ranked Pairs.
Ranked Pairs drops the strongest defeat that's the weakest defeat in
some cycle.

>
> > 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.

Because they can't all be allowed to exist if we want to find a
winner, and if we expect our winner to be someone who is unbeaten.
Some defeat has got to go.


>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.

If we drop weakest defeats till there are no cycles, is that what
you're saying that Condorcet suggested? What would its properties be?

>
> > 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.

I don't remember the exact words, but in an article in _Journal of
Economic Perspective_, for Winter '95, it seems to me that they said
that Ranked Pairs was Tideman's interpretation of Condorcet's
top-down proposal.

Due to the probability goals, it's true that Condorcet probably did
mean margins, regardless of what his method-wording says, when
interpreted by a French dictionary of his time. There's no disagreement
on that. I don't know why I didn't earlier say that, but it wasn't
from any intentional effort to cover up evidence against my
exclusion of margins from being Condorcet's method.

But if you're saying that Condorcet's drop-weakest proposal says to
drop the weakest defeat till there are no cycles, that's a radical
new interpretation. It seems that it would elect more winners than
DCD would. DCD was a method that I defined in Feb. 2000, that said:
Drop each cycle's weakest defeat. None of us propose it due to its
indecisiveness.

Mike Ossipoff

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