[EM] Condorcet cyclic drop rule

[Markus Schulze]

Dear Mike,

you wrote (7 Apr 2001):
> But I think most would agree that his (= Condorcet's) words were
> often un-specific enough so that we can still call PC & SSD
> "Condorcet's method", as well as Ranked-Pairs, whether defeat-support
> or margins. (And BeatpathWinner also, due to its equivalence with a
> version of SSD).

I don't agree that Condorcet's words were "un-specific." I rather
think that Condorcet mistakenly believed (1) that when he successively
eliminates the weakest defeat until there are no cycles anymore then
there will always be still enough defeats to calculate a unique ranking
and (2) that when he successively locks the strongest defeat then he
will have a unique ranking before a defeat locks in a cycle.

Condorcet's thoughts are rather erroneous than un-specific. And it is
quite speculative which election method Condorcet would have promoted
if he hadn't made this error.

But -to my opinion- a necessary (but not sufficient) condition for an
election method that wants to be called "Condorcet's method" is that in
those cases where Condorcet didn't erred the winner must be identical to
the winner of Condorcet's proposals. In other words: In those cases in
which (1) when one successively eliminates the weakest defeat until there
are no cycles anymore there are still enough defeats to calculate a unique
ranking and (2) when one successively locks the strongest defeat then one
will have a unique ranking before a defeat locks in a cycle, the winner
of this method must be identical to the top-ranked candidate of this then
unique ranking.

Markus Schulze