Kevin--
You said:
ROC is indeed a rank method. It's just one that fails anonymity.
I reply:
Or nondictatorship. It depends on whether I'm considered a voter. I was assuming that I wasn't a voter. (There'd be no need for me to vote in that method).
Of course failing nondictatorship is more extreme than just failing anonymity.
You continued:
What's the point of making exceptions for methods that don't accept a full ranking, when the omitted rankings wouldn't even make a difference in the result?
I reply:
That's exactly my point.
My criteria make no exceptions for any type of method. They apply uniformly to all proposable methods, without specifying anything about rules, and without any ridiculous fictions about any method's rules.
The person who's making an exception for Pluralty & Approval is the person who claims that it's necessary to pretend that their rules are different from what they are.
You can call Plurality's & Approval's nonranked rules "an exception", but it isn't an exception that I make. It's just the actual rules of those methods. To pretend that their rules are different from what they are, that would be "making an exception" for those methods.
You continued:
The methods that pose problems are those that require some input from the voter other than a ranking. Consider Approval, which arguably requires a cutoff in addition to the ranking.
I reply:
No, if you're going to pretend that Plurality allows ranking all the candidates, you can pretend the same thing about Approval. Approval simply differs by allowing a voter to equal-rank. Sure, and let voters equal rank at all rank positions--why not. Or rather _say_ that Approval allows that.
You continued:
Is it possible to say whether Approval meets Clone-Winner?
I reply:
Yes.
When ICC is defined in terms of sincere preference and stipulates sincere voting, like my CC, then Approval doesn't pass ICC. But Approval passes the ICC that Markus posted. I don't know if Approval would fail Markus's ICC if we used the ridiculous fiction that Approval allows the ranking of all the candidates. Maybe. I haven't checked.
You continued:
Unless we have specific rules about how the cutoff may move in response to the introduction of clones, I suppose we have to assume that Approval fails this criterion.
I reply:
I once asked what ICC assumes about how people vote. I asked, does ICC assume sincere voting, or that voting is undominated strategy, or that voting maximizes utility expectation by some possible set of utilities and probability estimates. Or does it just require that no ballot is changed when a clone is deleted from the election? It turned out that the assumption of sincere voting comes closest to the way that ICC is intended.
You continued:
For a more abstract example, suppose the method requires the voter to
label each candidate "red," "green," or "blue." Unless we have rules about how
and why labels may adjust in coordination with the rankings, we have to assume
that the method fails every criterion.
I reply:
Are you sure? A method meets the Majority Criterion if a candidate wins if more than half of the voters vote hir over all the other candidates.
No matter what color they vote hir, if s/he always wins if more than half of the voters vote hir over everyone else, then the method meets the Majority Criterion. If s/he can lose even though everyone votes hir over everyone else, then the method fails MC.
Those things are true regardless of what color people vote hir. Colors aren't part of the requirement or premise of MC. The failure-example-writer can configure color votes anyway s/he wants to, since they aren't mentioned in MC's premise.
But MC's requirement doesn't mention colors either. Of course the method's count rule might be strongly affected by color votes. If so, the failure-example-writer, being able to configure the color votes however s/he wants to, because they aren't mentioned in MC's premise, can try to find a combination of color votes, and whatever other kind of voting the method uses, in which a candidate loses even though everyone votes hir over everyone else.
And, by the way, in that hypothetical method, for all we know, your color assignments could have something to do with whether you're voting X over Y. If so, then the voters' color-assignments would have to be part of what the failure-example writer would have to configure. Even if there's a way to vote X over Y regardless of how you color anyone, the matter of whether you vote X over Y could still be affected by your color votes under some conditions. Aside from that, it could still be necessary, by the method's rules, to configure the coloring in a certain way in order to make a candidate lose when more than half of the voters vote hir over everyone else.
But if someone can show an example in which more than half of the voters vote a candidate over everyone else, and that candidate loses, then that person has shown that the method fails MC. And if it can be shown that there's no such example, then it's been shown that the method passes MC.
That's true regardless of the method's color votes.
Mike Ossipoff
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