Explaining Condorcet (was Re: Condorcet sub-cycle rule)

[David Marsay]

Steve Eppley, in response to a note of mine, wrote:

> One might point out that the widely-accepted Robert's Rules of 
> Order uses, as its basic majority rule procedure, a method which 
> rigorously satisfies both the Condorcet criterion and the Smith 
> criterion.  Which suggests that it shouldn't really be that hard 
> to convince folks of the merits of Smith//Condorcet.

The Condorcet criterion is 'obviously' a 'good thing'. I regard the 
Condorcet METHOD as being good too. Unlike Smith, the Condorcet 
method is considerably stronger than the Condorcet criterion. If it 
is easy to convince people of the METHOD, we should do so, as it 
would save a lot of nugatory discussion.

I propose a Condorcet+ criterion, which the Condorcet method 
satisfies.

Given options X, Y I denote X >m Y whenever there exists a directed 
path from X to Y such that in each link the first has a plurality 
of at least m over the last. The criterion is that if, for some m, X 
> m Y but not Y >m X, then X >> Y (is preferred overall).

Condorcet gives many arguments in support of this criterion, but - 
like me - seems to regard it as so 'obvious' that he fails to create 
a case sufficient to convince a sceptic. My remarks about Dodgson and 
Kemeney were intended to suggest that their independently obtaining a 
similar method might be regarded as strong support.

Incidentally, Arrow in "Social choice and individual values" is 
commonly regarded as showing that no general voting method is 
possible, but in the second edition he refers to Black's "The theory 
of committees and elections" and refers to Dodgson's method as 
"extremely worthwhile" and notes that "in principle, and especially 
with computing machinery, the criterion itself provides a method of 
choosing candidates. I do not known whether there is a simple way of 
characterizing this principle." A challenge!
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