Markus--
You said:
so far as election methods are defined only on the cast preferences and not on the sincere preferences, whether a given election method satisfies a given criterion must be reflected in the way this method uses the cast preferences. Therefore, there is no need to include the sincere preferences in the definition of a criterion.
I reply:
No, that doesn't follow. Yes methods are defined on cast ballots. No, criteria needn't be in the form of instructions about how a method uses those cast ballots. You've said that you prefer that, and I don't deny that you prefer it. But you haven't shown us why a criterion must be in the form of an instruction for how a method uses the ballots. A criterion can be about something that should or shouldn't happen.
You say that there's no need o mention preferences, meaning presumably that it's always possible to write an equivalent criterion that only mentions cast ballots, a "votes-onlyl" criterion.
But you didn't succeed in doing so:
Later in your posting you wrote a criterion that you presumably imply is equivalent to my SDSC. But it isn't. Plurality meets your criterion. Plurality doesn't meet SDSC.
More details about that where this message replies to that part of your message.
You said:
I would call
"If more than half of the voters prefer alternative y over alternative x, then that majority must have some way of voting that ensures x will not be elected and does not require any of them to rank y equal to or over any alternatives preferred over y."
the "motivation" of this criterion and
"Any ordering of the alternatives must be an admissible vote, and if more than half of the voters rank y over x and x no higher than tied for bottom, then x must not be elected."
the "definition" of this criterion.
I reply:
You said "...rank y over x". What if the method isn't a rank method? Or does your critrerioin apply only to rank methods? If so, then it isn't equivalent to SDSC.
Or maybe when you said "rank y over x", you meant "vote y over X". Of course, when writing a criterion, it's better if youi say what you mean. If you mean for "rank" to mean "vote", then you've got to tell us what you want "rank" to mean.
And you haven't stated a definition for voting y over x anyway.
Maybe you have a definiiton, special for Plurality, that says that if you vote for y, then you're "ranking" y over everyoen else. But you didn't tell us that, and so, again, your definition isn't complete. Additionallly, if that's what you were trying to say, your definitions require a special definition for Pluralilty. None of my definitions require a special definition for a particular method. Theyi all apply to all proposed methods, without method-specific definitions.
So, from the above, your criterion either is unequivalent with SDSC because your crirterion applies only to rank methods, or else your definition is incompete, and you haven't defined a criterion at all.
But, let's pretend that you've said that you said "vote y over x", and that you've specified Richard's or my definition of voting one candidate over another, or that you've stated the Plurality-specific definition of ranking that I wrote above. Your criterion still is not equivalent to SDSC. That's because now Plurality meets your criterion.
Let me copy your criterion definition here:
"Any ordering of the alternatives must be an admissible vote, and if more than half of the voters rank y over x and x no higher than tied for bottom, then x must not be elected."
Say the method is Plurality, and that more than half of the voters vote for y. Then x won't win.
Therefore Plurality meets your criterion. Your criterion is not equivalent to SDSC.
Your "motivation" says something that roughly resembles the goal of SDSC, but your criterion doesn't deliiver what your "motivation" promises.
You really should respect the members of this list enough to check your statements before you post them, so that everyone's inbox-space isn't wasted with criteria that aren't equivalent to what you want them to be, and my demonstrations of that nonequivalence.
Also, maybe you're being a little too ambitious, if you're trying to write something equivalent to SDSC.
That's why I suggested that you start with the more familiar Condorcet's Criterion.
You didn't write a votes-only critrerion that's equivalent to SDSC.
Can you or can you not write a votes-only criterion that's equivalent to my Condorcet's Criterion?
Mike Ossipoff
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