[EM] The Condorcet question

[MIKE OSSIPOFF]

Rob--

I'm sorry to be so late in replying; It's been several days since I've
had a chance to go on the computer.

Also, I should have read your reply to that person before writing mine,
to avoid duplication. But when your reply wasn't in the same posting
as his question, I assumed that you'd forgotten to include it. It wasn't
until I'd already selected this reply screen that it occurred to me that
your subsequent message is probably your reply.

Forward this reply to that person. No need to remove my name.

Anyway, here's my reply to that person's question:

It's true that, in the example, the socialist faction could win by
strategic order-reversal. But, with the winning-votes Condorcet versions, 
that offensive strategy can steal the election from the
middle faction only if the middle faction co-operate in their
victimization by trying to help those who are victimizing them.

In general, in wv, with offensive order-reversal, you can only steal
the election from people who are trying to help you. I hope you're
proud of yourself :-)

Of course that's one reason why you wouldn't use that offensive strategy. 
Another reason is that the middle voters would never rank
the socialists 2nd again. A third reason, for me, would be that
such devious election-stealing would discredit Condorcet's method.

But there's a 4th reason too: If your intended victims don't co-operate in 
their victimization, then your offensive strategy will backfire
by electing the authoritarian, your last choice. Again, in general,
that's what happens if the victims don't co-operate with you.

Whan Nash equilibrium is defined for voting situations, it's been shown 
that, with Condorcet(winning-votes),  when there's a Condorcet candidate
(a candidate who, when compared separately to each one of the others,
is preferred to him/her by more voters than vice-versa), there's always
a Nash equilibrium in which the Condorcet candidate wins, and no one
order-reverses.

That is not true of single-winner STV. Nor is it true of Condorcet
versions other than the winning-votes versions.

Winning votes refers to a way of measureing defeats in Condorcet's
method. By winning-votes, if A beats B, the strength of that defeat
is measured by the number of people ranking A over B. Some would measure
that defeat by the _margin_ of defeat, but that version has all of
the strategy problems that single-winner STV advocates attribute to
Condorcet. It's as bad as you say it is. So it all depends on how
Condorcet's method measures defeats.

For more strategy criteria, for evaluating single-winner voting systems,
I refer you to http://www.electionmethods.org   Select the
technical evaluation page.

By the way, that Nash equilibrium guarantee that I mentioned also
applies to the Approval voting system, the method that uses the old
FPTP ballot, but lets people mark as many names as they want to,
giving one whole vote to each candidate whom they mark.

You mentioned a possible temptation to order-reverse strategically
in Condorcet. I answered that objection, but I also point out that
single-winner STV often creates a strategic _need_ to order-reverse
, when that's the only way to protect a needed compromise from immediate
elimination, to prevent the victory of one's last choice. Condorcet(wv)
doesn't create that strategic need to anything like the degree that
single-winner STV does. With single-winner STV you'll often need to
bury your favorite to protect your compromise. Approval, by the way,
will never give anyone incentive to do that.

Mike Ossipoff



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