[EM] Reply to Examples & Criticisms
dfb at bbs.cruzio.com
Sat Mar 23 16:41:12 PST 1996
An opponent of Condorcet's method has sent some of you his arguments
against it, with "bad-examples". I understand that he intends to
post this to EM, and so I'm sending my reply to it now.
These criticisms are largely based on "bad-examples". But Bruce
surely knows as well as I do that, for any method, examples can
be devised in which that method will dramatically fail some standard
other than the standard on which it is based. For instance, Fishburn
has written a bad-example for Copeland's method, the method proposed
by Bruce. I'll post that Copeland bad-example in a subsequent
letter, and perhaps then improve on it too.
Anyway, you'll notice, when you receive Bruce's Condorcet bad-examples,
that in every one of those examples, every alternative has a majority
against it. That's no accident: That's the only way that Bruce could
make Condorcet elect something with a majority against it, and the
goal of the examples included having the winner by Condorcet's method
be beaten by a majority, sometimes a big one (which required that the
other alternatives all be beaten by an even bigger majority).
The other goal was to make the winner by Condorcet's method be beaten
by many other alternatives. That's very easy, since Condorcet counts
voters, not candidates. Condorcet counts how many people rank another
alternative over you, not how many candidates you beat. Counting
votes makes more sense than counting candidates, and carries out
the goal that led us to want single-winner reform in the 1st place:
getting rid of the lesser-of-2-evils problem.
But all these examples really show is that Condorcet doesn't count
candidtes--it doesn't count how many alternatives a particular
alternative beats or is beaten by. In other words, the examples
demonstrate that Condorcet isn't Copeland. Excuse me, but why
should Condorcet be Copeland. Bruce criticizes Condorcet's method
because it doesn't pick its winner by the same standard that
Copeland uses. The examples & the criticisms based on them are
based on that.
And, in order to make 1 alternative barely beat the others by
Condordet's method, Bruce's examples all have a near tie by
Condorcet's method. All the alternatives are about the same in
regards to the majority by which some other alternative beats them.
And yet, in each example, 1 alternative is beaten by every 1 of
the others (except for the last example, where it's beaten by all
but 1). If it seems a little odd to you that when the alternatives
hardly differ at all in regards to the majority by which something
beats them, but one of them is so unpopular that everything beats
it, that seems odd to me also. Bruce says that example 4 is a
strange result. I agree, and in fact there's something strange
about all the examples, as I've just described. Inexplicable
I'm going to resist talking about the academic standards here,
and save that for a separate letter. At least the Condorcet Loser
Criterion & the Smith Criterion & the Generalized Majority Criterion.
These standards, & their relationship to Condorcet are the subject
of a whole letter.
But I'd like to just mention the Majority Loser Criterion here.
Only to mention that violating that criterion requires electing
somethign with a majority against it, which, as I said can only
happen in Condorcet if everything has a majority against it.
Violating the Majority Loser Criterion, electing something that's
the last choice of a majority, but that criterion is overkill, since
it's undesirable to elect something with a majority against it at all.
What the examples don't show is that Copeland can easily elect something
that has a majority against it, when it's the only alternative with
a majority against it. I believe that's what's to be avoided; that's
the important thing. What the Majority Loser Criterion adds to that
is something about _how many_ alternatives the voters in that majority
ranked over the alternative in question. So, again, we're counting
candidates, and judging Condorcet by Copeland's standard. Why should
Condorcet be expected to go by Copeland's standard.
Here's the standard that's important to me:
A set of voters consisting of a full majority of all the voters
have the power to make happen whatever they agree on. But they should
be able to do so without having to reverse preference orderings
or insincerely rank alternatives equal. In fact, as often as possible,
they shouldn't have to use strategy at all, but should be able to
This is a generalization of the usual Majority Criterion, which
merely says to elect someone if a full majority rank them 1st.
Because, there are other things a majority can want than to elect
a common 1st choice. If you're part of a Nader + Clinton majority
who want to defeat Dole, and rank Clinton over him for that reason,
then you'd like that majority to succeed even though you've ranked
Clinton 2nd instead of 1st. Sounds easy maybe, but most methods do
a lousy job of it. Copeland does poorly at it. The goal in this
paragraph can be recognized as the lesser-of-2-evils problem,
the strategy problem that so dominates the voting of progressives.
Well worth avoiding, wouldn't you agree? The generalized majority
standard in the previous paragraph is really a re-statement of
the goal in this paragaph.
Condorcet's method, because it counts "votes-against", rather
than counting candidates, like Copeland, does the best possible
job of meeting that goal, for a 1-balloting method. In fact,
with Copeland, absolutely no strategy is needed unless significant
numbers of voters are attempting the devious offensive strategy
of "order-reversal" (falsification of a preference ordering),
a strategy well-deterred by Condorcet's method & unlikely to
happen on a scale sufficient to change the election result.
I mention my majority standard here because Bruce invokes "majority
rule" in connection with the Majority Loser Criterion, either saying
or implying that Condorcet's method is violating majority rule in
his examples. Nonsense. How do you comply with majority rule when
every alternative has a majority against it? Pick the one with the
smallest majority against it? That's what Condorcet does. The unfortunate
fact, in those contrived examples, is that, since everything has something
else ranked over it by a majority, the election of anything violates
majority rule. That's why a number of single-winner reform advocates
propose, in a public election where that happens, that we disqualify
all the candidates & hold a new election with new candidates.
I emphasize that Bruce's examples will appear dramatic to you, because
they're devised so that the winner chosen by Condorcet not only
doesn't comply with the candidate-counting standard, but it violates
it in a very big way--big enough to stand out very prominently, to
get your attention. You're supposed to say "Hey, that doesn't look
right!". But I've talked here about how easy it is to make a method
violate a standard that isn't its own, and violate it in a big way.
One last thing: If desired (though it isn't necessary) Condorcet
could be modified by simple refinements so that it would meet
the academic standards, including the ones that Bruce criticizes
it for. For instance there could be a simple rule that says
"Anyone beaten by everyone else is disqualified". Bruce might say
that sounds like a "patch". Sure. To make a method meet more than
1 standard, it can be necessary to combine more than 1 rule. If
only there were such a simple patch that would fix Copeland's
failure in regards to the lesser-of-2-evils problem & the need
for defensive strategy.
Another refinement for Condorcet, to meet academic criteria, would
be, in the situation where no 1 alternative beats each one of the
others, because several beat eachother (& everything else), we simply
say to limit the choice to that group of alternatives that beat all
the others. If a group of candidates all beat all the others, then
choose from that group. Bruce says that's too complicated to offer
you. I disagree.
In example 4, Bruce shows that, even with refinements like these,
Condorcet still is noticibly different from Copeland, and can
be make to violate Copeland's standard in a noticible way. Amazing.
But when the refinement of the previous paragraph is added,
Condorcet meets all the standards that are important to the
academics, including the ones that Bruce criticized it for not
I'd continue, but some of the things I'd add really belong
in separate letters.
There will be several letters, of which this is the 1st:
1. Reply to Examples & Criticisms
2. My standards (yours too) & Condorcet's method
3. Condorcet vs Copeland (direct comparisons)
4. Copeland Examples
These letters will be sent about one every days, or every few
One last thing: The strongest statements against Condorcet's method
in Bruce's letter are preceded by the word "Arguably..." Yes, but
anything can be argued. But though anything can be argued, there
are arguable statements whose arguments won't hold up to rebuttal.
Ok this is really the last thing in this letter: I don't want to
sound hostile or angry or critical of Bruce. My purpose is to
refute his arguments. If that sounds argumentative when I do it,
or course it is. But it implies no criticism of Bruce himself.
Argument is an essential part of debate, which in turn is
necessary to make a collective choice, such as the choice of
which single-winner method is the best. Besides, I didn't ask
Bruce to send out e-mail to the effect that arguably Condorcet's
method shouldn't be used for any kind of vote. I'm not saying
that he shouldn't say that, just because it's a method that I
propose. But no one should be surprised if I criticize the arguments
used to support that claim. That's what discussion is about.
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