[EM] New criterion: The Co-operation/Defection Criterion

[MIKE OSSIPOFF]

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