Correct Condorcet Criterion

[Mike Ossipoff]

I forgot to mention: There is a way of writing the Condorcet
criterion in such a way that some methods meet it:

A method meets the Condorcet Criterion if & only it will always
pick an alternative if that alternative, when compared separeately
to each one of the others, is ranked above it on more ballots
than vice-versa.

This vote-based, rather than preference-based defintion is met
by all the Pairwise methods, including plain Condorcet, Smith//Condorcet
& Copeland.

This is what academic authors mean to say when they define the
Condorcet criterion.

But still, by defining it as they do, in terms of preferences,
that reveals the goal that is felt by those authors: the 
election of the Condorcet winner (the alternative which,
when compared separately to each one of the others, is
preferred to it by more voters than vice-versa). 

As I said, this can meaningfully be said as a standard, but
not as a criterion: How well does a method do at electing
the Condorcet winner?

As I said: Copeland does a lousy job. Condorcet, for all the
reasons that I've given, does a very good job of it.

***

As I said, it isn't just Bruce who uses imprecise & not really
workable definitions for the academic criteria. It's widespead
practice among academic authors, based on what I've run across.

And it isn't just Bruce who likes Copeland's method. Though
academics tend to avoid saying what's best, Copeland seems
to be a major academic favorite, judging by the good things
said about it in academic articles.

So isn't it interesting that a favorite method of the academics
(& _the_ favorite of some of them) does so badly by the
academics' own standards, as expressed in some of their
over-optimistic, unattainable criterion definitions?


Mike



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