Co-operation/Defection Criterion (CD):
Premise:
A majority prefer A and B to everyone else, and the rest of the voters all
prefer everyone else to A and B.
Candidate A is the Condorcet candidate
Voting is sincere except that the B voters (voters preferring B to everyone)
else refuse to vote A over anyone.
Requirement:
The Condorcet candidate wins.
[end of CD definition]
I’m only aware of one method that meets CD: MMPO.
If {A,B} were replaced with a larger set of candidates, would any method be
able to meet the criterion?
CD is based on the Approval bad example that I posted a few days ago. When
posting it, I mistakenly said that DMC doesn’t fail in that example. DMC fails
in that example.
Of course the Approval bad-example was a 3-candidate example. I’ve generalized
it as much as possible, while retaining enough similarity to the example for it
to be able to discriminate between methods as did the Approval bad-example.
The Approval bad-example indeed is bad (though forgivable for the simple
Approval method). The B voters are successfully taking advantage of the A
voters’ co-operation.
But we can expect and get more from a rank method.
Of course, the solution for failing methods is: Before the election, the A
voters publicly point out that A is the Condorcet candidate, or has more
support than B does. The A voters make it clear that they aren’t going to
support B in the election.
But, with MMPO, A wins anyway, even if the A voters co-operate and the B voters
defect.
If you notice anyone using the Approval bad-example against Approval, ask them
what method _doesn’t_ fail in that example. Most likely they won’t be able to
name one.
And even MMPO only passes because {A,B} is only a 2-candidate set.
James claims that Approval is “vulnerable to strategic manipulation”. He’s no
doubt heard that statement from various academics. In the Approval bad-example,
yes, it’s reasonable to say that the B voters are successfully using offensive
strategy against A, the Condorcet candidate, since they're intentionally taking
advantage of the A voters' co-operation. But what James misses (or just doesn’t
like to talk about) is that nearly all methods likewise fail in that example.
In particular, Plurality fails it too. Nearly all methods are “vulnerable” to
that same offensive strategy by the B voters.
If James is going to criticize Approval for the Approval bad-example, then
James needs to be an advocate of MMPO.
I’ve said this many times before, but academics and IRVists still keep
complaining that some methods are vulnerable to strategy.
What they miss (or would like their readers to miss) is that all
nonprobabilistic methods are strategic. All need defensive strategy, at least
sometimes.
WV and MMPO rarely need it, but sometimes could, if offensive order-reversal
were attempted on a very large scale.
In an election with Nader, Democrat, and Republican, (and some candidates more
disliked by Nader voters and Democrats), even if all the Democrat voters prefer
the Republican to Nader and rank accordingly, the number of Republicans using
offensive order-reversal against the Democrat would have to be greater than the
entire number of Democrat voters, in order for the offensive order-reversal to
be able to succeed—even if no one uses any defensive strategy.
And defensive truncation by even a tiny fraction of the Democrats would thwart
and penalize the offensive order-reversal, by electing Nader.
What distinguishes Plurality and IRV is that those two methods have a drastic
need for defensive strategy even without any offensive strategy being
attempted. And that defensive strategy takes the form of favorite-burial.
The academic s who complain about Approval’s vulnerability to strategic
manipulation are probably trying to imply that Plurality is better, because it
has no offensive strategy—even though Plurality has the most drastic and
always-present need for the most drastic form of defensive
strategy—favorite-burial, even without any offensive strategy being used.
Anyway, in the Approval bad-example, the same situation exists with Plurality,
except that it’s worse: If the B voters say that they are going to vote for B,
even though A has more support, then the A voters can’t keep C from winning
unless they vote for B instead of for their favorite.
If, in Plurality, the B voters make it known that they won’t vote for A, though
A has more 1st choice voters, that would have to be called offensive strategy,
as I’ve defined it, if you call it offensive strategy when it’s used in
Approval.
As I said, the A voters, in Plurality or Approval, or any CD-failing method,
would need to declare that they’re voting for A and not for B.
Mike Ossipoff
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