Definition of "Pairwise Method"

[Mike Ossipoff]

Replying to Bruce:


1. "Condorcet winner"  is usually used to mean an alternative which,
when compared separately to each one of other alternatives, is preferred
to it by more voters than vice-versa.

It can be worded other ways, of course. It's the alternative that
would beat each one of the others if every voter sincerely ranked all
of the alternatives (except, of course for alternatives unranked because
you like them less than the ones you rank, and because you dislike them
all equally).

And it's sometimes defined as the alternative which would beat each
one of the others in separate 1-on-1 elections in which voterss vote
sincerely. (Of course there's no reason not to vote sincerely in a
1-on-1 election).

All these definitions are equivalent.

"Condorcet winner" shouldn't be used to mean the winner by Condorcet's
method. Though Condorcet's method does the best job of electing Condorcet
winners when there is one, certainly much better than Copeland or any
Copeland version, it's still best to keep "Condorcet winner" and
"winner by Condorcet's method" separate.


2. Bruce's recent letter shows that Bruce's meaning for the term
"Condorcet's method", and my meaning for that term differ by a lot
more than just the fact that Bruce would count preferences that aren't
expressed.

There's also the fact that, as Bruce stated his version, Bruce would
count votes-for instead of votes-against. Big difference.

Bruce said the winner by Condorcet's method, as he uses the term,
is the alternative with the largest minimum over j, of r(i,j).
Unless I misunderstand the formulese, this means the alternative which
has the largest vote for it in its pairwise comparisons with the
other alternatives.

Bruce has asserted his right to define Condorcet any way he wants to.
But the question is--why define it differently from its proponents?

Bruce has said in an e-letter to some EM members that arguably Condorcet's
method shouldn't be used for any kind of elections. You've just told us
what you mean by Condorcet's method. And I agree with you that, as you
define Condorcet's method, it shouldn't be used for any kind of elections.

But since we're interested in comparing the merit of methods, and some
of us propose Condorcet, and you propose Copeland, or your Regular-Champion
version of Copeland, what possible purpose could you have in defining
a different meaning for "Condorcet's method", when it isn't even what
you're proposing. I repeat: How about letting us define our proposal?

***

I should also add that Condorcet's own statement of his proposal
spoke of votes-against, not votes-for. So the method that Bruce is
callling "Condorcet's method" really doesn't qualify for that name.
Call it "Anderson's method", or "Anderson's 2nd Method", but it
just isn't Condorcet's method, not if we go by what Condorcet
proposed. Though Condorcet wasn't as specific as some would like,
he did speak of votes-against, not votes-for.

Similarly, the translation of Condorcet's words, in Duncan Black's
book, didn't say anything about counting preferences that no one voted,
inventing un-expressed preferences. So if you're going to do that, kindly
name it something else, because it isn't Condorcet's method.

***

to be immediately continlued

***

Mike





 

--