[EM] Condorcet cyclic drop rule
bcretney at postmark.net
Sun Apr 8 12:31:53 PDT 2001
As to what I believe Condorcet meant his method to be, the following
has to be kept in mind. Condorcet appears to have believed that you
could partition the majorities into two groups, with the second group
all lower than the first. He believes that for some such partition,
the first group defines a unique ordering of the candidates. Of
course, he never explicitly states this assumption. But it is the
only way his descriptions make sense.
He gives at least two different descriptions of his method. Either
start with the highest majorities, and work your way down until you
have a complete ordering, or start with the lowest, and drop them
until the contradictions are all gone (and you are left with a
complete ordering). Under Condorcet's assumption, these descriptions
are the same, fairly sensible, and unambiguous.
Unfortunately, Condorcet's assumption is false, so his wording is
confusing, and procedure is impossible to follow in some cases.
However, his meaning is still clear, if you carefully analyze it, and
don't impose modern assumptions on it.
Mike, some of your comments seem to suggest that you think I am taking
this interpretation because I advocate this procedure. There's no
link between the two. The precise method Condorcet describes simply
cannot be carried out.
Notice Condorcet's words in the following:
> > Condorcet's (1785) seminal paper expresses the idea that a
> > > who would defeat each of the others head-to-head should win the
> > > election. If no such candidate exists, then large majorities
> > > take precedence over small majorities in breaking cycles. In his
> > > own words, the general rule was "to take successively all the
> > > propositions that have a majority, beginning with those
> > > the largest. As soon as these first decisions produce a result,
> > > should be taken as a decision, without regard for the less
> > > decisions that follow."
Once again Condorcet appears to be making the partition assumption.
Under that assumption, this method is precisely the same as given in
his other descriptions. It doesn't reflect an evolution in thinking,
just a different way of expressing the same idea.
I think that Ranked Pairs follows naturally from the principles
suggested by Condorcet. He wants to drop lower majorities in favour
of higher, in order to find a complete ranking of the candidates. He
seems to assume that the majorities he is dropping would otherwise
form contradictions with higher majorities that he is not dropping, or
that he can safely drop them because they are redundant given
majorities that he is not dropping. If he didn't make the assumption
that successive dropping would have that property, he might very well
have made it an explicit part of the dropping rule. That is, that
majorities should only be dropped if they would otherwise form a
contradiction with higher majorities that aren't being dropped. Of
course, that is Ranked Pairs.
So, Ranked Pairs is a natural extension of Condorcet's principles. It
is a method that he might very well have proposed, had he noticed his
erroneous assumption. It agrees with his process in those cases where
his process works (as do others). In a loose sense, it could be
termed an interpretation. On the other hand, I think it is quite
clear that he did not mean Ranked Pairs, or any other currently
advocated method when he described his procedure. So, in that sense,
none of these methods are correct interpretations.
My preference would be to reserve the term "Condorcet's method" for
his procedure of finding the Condorcet winner, where one exists, since
that procedure actually works. Anyone who is using a method that
meets the Condorcet criterion is using Condorcet's method (although
perhaps implicitly). There has been some talk that "Condorcet's
method" has been used to mean MinMax in some academic journals. It's
unfortunate if that is the case, because it gives a misleading
impression of what Condorcet actually advocated. However, we haven't
had any actual quotes presented to the list yet.
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