It isn't quite Condorcet's method.
First, about how to treat short rankings, if you've ranked X
and you haven't ranked Y, then it's reasonable to say that you've
ranked X over Y. I hope that's how that's interpreted in the
debian count rules.
The rank-counting procedure now in use by debian carries out
Condorcet's suggestion that if there's 1 candidate who,
when compared separately to each one of the others, is ranked
over him/here by more voters than vice-versa, then that candidate
should win.
That's called "Condorcet's Criterion".
But it isn't really Condorcet's method, because Condorcet
proposed a complete method, a method that specified what to
do when there isn't 1 candidate who pairwise-beats each one of
the others.
Actually, he made 2 proposals about that, and either could
be called Condorcet's method. But of course there are other
ways of solving "circular ties", where no 1 candidate beats
each one of the others:
Copeland suggested that we subtract the number of pairwise-defeats
that a candidate has from the number of pairwise-victories that
he has, and call that his Copeland score. The winner is the
candidate with highest Copeland score. There's often a tie.
Dodgson suggested that we elect the candidate who could be made
to beat everyone by reversing the fewest individual pairwise
preference votes.
Black suggested that we use Borda's point system when there's
a circular tie.
And so on...
The method that debian is currently using, solving circular ties
by the Alternative Vote elimination system is equivalent to
something proposed by George Hallett, in a book in 1926, and
so it could be called "Hallett's method".
What all these methods have in common is that they're
pairwise-count methods, and they're Condorcet Criterion methods,
meaning that they comply with Condorcet's Criterion. But they
aren't Condorcet's method. They're Copeland's method, Dodgson's
method, Black's method, and Hallett's method. (Incidentally,
Dodgson was the author better known as Lewis Carroll).
What Condorcet proposed were 2 methods that stepwise drop
weakest defeats.
I described several interpretations of what Condorcet meant,
when I wrote to this mailing list about half a year ago.
Since it's so brief, let me repeat one of the circular tie
solutions that I defined that time, a good interpretation of
what Condorcet meant with one of his proposals:
Sequential Dropping (SD):
Drop the weakest defeat that is in a cycle. Repeat till there's
an unbeaten candidate.
(B's defeat by A is measured by how many people ranked A over B).
***
Condorcet's method has many advantages over the other
circular tie solutions, in regards to majority rule, and
avoidance of strategy problems, such as the lesser-of-2-evils
problem and the spoiler problem.
I'll refrain from repeating here the somewhat wordier definition
of the other interpretation of Condorcet's "bottom-up" proposal,
because I defined it here about half a year ago. I called it
Schwartz Sequential Dropping (SSD).
The most widely accepted interpretation of Condorcet's other
stepwise weak-defeat-dropping proposal is slightly wordier:
Drop the strongest defeat that's the weakest defeat in a cycle.
Repeat till there are no cycles remaining.
Probably the motivation for that isn't obvious, so let me tell you
its original wording:
Tideman's method:
1. Arrange all the defeats in a list in order of their strength.
2. Starting with the strongest defeat, consider, in turn, each
defeat in the list. If a defeat is in a cycle with stronger
defeat, then drop it.
3. Continue down the list in that way till no cycles remain.
***
But actually, it was originally worded in terms of "keeping"
or "locking-in" defeats, rather than dropping them:
1. Arrange all the defeats in a list in order of their strength.
2. Starting with the strongest defeat in the list, consider, in
turn, each defeat in the list. Keep the list being considered
if it isn't in a cycle with stronger defeats that have been
kept. Otherwise, skip it.
3. Continue down the list in that way till no cycles remain.
***
So, in a meaningful sense, one is keeping all the strongest defeats
possible.
***
For committee voting, SSD & Tideman are excellent.
In committees, where there are so few voters that pairwise ties
or equal defeats are likely, Tideman has one known advantage
over SSD:
A "clone set" is a set of candidates who are adjacently-ranked
in every voter's ranking. And let's say that a clone set must
have more than 1 member.
Independence from Clones Criterion (ICC):
Removing a candidate from a clone set shouldn't change the matter
of whether the winner comes from that clone set.
SSD, but not Tideman, can fail ICC in small committee elections
where there are pairwise ties or equal defeats. In the example
that I'm aware of, this just means that there are situations
where Tideman will return a tie between two clone sets, while
SSD is decisive and picks a winner, and the matter of which
clone set the winner comes from can be influenced by internal
defeats in the clone sets. The purist doesn't like that, and
prefers Tideman's tie, and its resort to a random tie-solution.
But if SSD's choice seems arbitrary to the clone-purist, maybe
it could be said that it's no worse than flipping a coin, unless
the tied clone sets situation is considered so likely as to
influence people's voting, or to deter "clone" candidates from
running.
Anyway, I've defined SD, SSD, & Tideman. The latter two
are considered better when pairwise ties or equal defeats are
likely, in small committee voting. Tideman satisfies the purist
who wants absolute compliance with the clone criterion, even
under small-committee conditions.
***
Well, now that I've written such a long letter, and defined
SD & Tideman (in 3 wordings), why not repeat the definition of
SSD:
1. an "unbeaten set" is a set of candidates none of whom are
beaten by anyone outside that set.
2. An "innermost unbeaten set" is an unbeaten set that doesn't
contain a smaller unbeaten set.
SSD:
Drop the weakest defeat that is between members of an
innermost unbeaten set. Repeat till there's an unbeaten
candidate.
***
If members of debian want to perfect their voting system,
then I suggest changing the count rule, the circular tie
solution to SD, or, especially, SSD or Tideman.
Though I posted the criteria that these methods meet, and which
distinguish them from other pairwise-count methods, I'll
re-post them, or send them by individual e-mail, upon request.
Mike Ossipoff
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