Bruce's truncation example

[Mike Ossipoff]

Bruce said, "There may be good reasons for arguing that this
example is inconsequential...".  True.

What Bruce has shown with his example is that when there's a
Condorcet winner, it's still possible for some voters to create
a circular tie by truncation (or order-reversal, or staying home).
That isn't news. Bruce, in his example, gave the Condorcet winner
a plurality, so that it would win in Regular-Champion, and 
contrived the numbers so that the truncators' candidate would
win by Condorcet count.

Notice that the truncators' candidate doesn't have a majority
against him. That's no accident. If he did, Bruce wouldn't have
been able to make him win by truncation when there's a Condorcet
winner. Bruce knew that. 

That's the difference between Condorcet & Copeland in an
example like that. With either method you can make a circular
tie by truncation. With either method you can juggle the numbers
to make the candidate win that you want to win. Except that
with Condorcet you can't make a candidate win with a majority
against him when there's someone who doesn't have a majority
against him. For instance, when there's a Condorcet winner
(who can't have a majority against him due to truncation).

And that's the time that it would be particularly undesirable
to have B win by truncation, when there's a majority against him,
since that's a violation of majority rule. That more important
situation is where Copeland screws up & Condorcet doesn't. 

Bruce's little table at the end of his letter is quite dishonest.
He wanted to impress you by showing you that in that example
(where Bruce gave C a plurality)  C wins no matter what
strategy is used by B voters. As if Bruce didn't know that
it could just as easily have been the opposite, with Copeland
consistently electing B. Did I say "just as easy"? No, it would
be easier for Regular Champion to screw up here in a big
way, because it would just as soon elect B with a majority
against it when no one else has a majority against him--screwing
up when it matters more. Bruce didn't show Condorcet violating
majority rule, because he couldn't. But he could with Copeland.

To show that, why don't I just repeat the example I used
before:

Sincere preferences:

40%: Dole, Clinton, Nader
25%: Clinton, Dole, Nader
35%: Nader, Clinton, Dole

Clinton is Condorcet winner.

Dole voters truncate:

40%: Dole
25%: Clinton, Dole, Nader
35%: Nader, Clinton, Dole

The truncation creates a circular tie. Dole wins easily
by Regular-Champion, by having a plurality. But he also
has a majority against him, and there's no way the truncation
can make a majority against Clinton. Clinton wins in Condorcet.

With Regular-Champion, Dole won even though he's the only
candidate with a majority against him. How's that for
majority rule?

***

About precisely-stated criteria, I hope I've shown that
there are precisely stated criteria that Condorcet meets
and which Copeland fails, and which we'd agree to be important--
like lesser-of-2-evils & majority rule.

And I hope I've also shown that Bruce & other academics haven't
been that precise in defining their criteria, and that when
those criteria are re-written as standards, because they
can't be useful criteria, it's Copeland & Regular Champion
that fail them, and it's Condorcet that does the best byk
those standards--the academics' own standards.

***

Mike








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