Paul said:
I've argued before that the uses of the terms "preference" and "sincere preference" on the list have treated the terms as "undefined terms"
I reply:
I posted a definition of "prefer" a few days ago.
Paul continued;
but have been applied ambiguously, which results in some confusion about what when and how they are applicable.
I reply:
I haven�t yet gotten around to wading into your confusion-filled angry postings about that. I don�t guarantee that I will. But if you say someting, somewhere in that mess, that speaks to something that I said, in my justification of using "prefer", then I�ll reply.
Paul said:
So for the purpose of analyzing election methods, we can assume that a method satisfying condition 1 can at least be aware of "sincere preferences"
I reply:
You didn�t say what you mean by saying that a method is aware of something.
Paul continues:
, and we can DEFINE "sincere preferences" to be the ballots cast if the method meets condition 1.
I reply:
Ok, now we get to your definition of preference. Sincere preference is the ballots cast if the method meets the following condition:
1. There exists at least one element of B that includes all members of P(v,A) and no members of P*(v,A) for any member v of V
In other words, for each voter there�s a ballot that has all of his/her acceptable alternatives and none of his/her unacceptable alternatives.
Say the method is Plurality. Say there�s one voter who considers more than one candidate acceptable. No ballot includes more than one candidate, because such a ballot would be illegal in Plurality. (or are you including illegal ballots that are thrown out?). Since there�s no ballot that includes all of that voter�s acceptable candidates, then that election�s ballots are not sincere preference, by your definition of sincere preference. Correct?
So, if you consider 2 candidates acceptable, and the method is Plurality, then the ballots of that election are not a sincere preference. And if your set of acceptable candidates is empty, and every one of the ballot votes for someone, then, again, the election�s ballots are not a sincere preference.
That�s what you mean by sincere preference, isn�t it? Because that�s what you said.
It isn�t entirely clear what your definition would be useful for.
Would you mind if I suggest that you might not get so mucked-up if you state your definitions in English, instead of trying to use a notation that you don�t understand?
This is like that cartoon, of a man and a woman in a French restaurant, where, on the woman�s plate is an old shoe, and on the man�s plate is a toy train locomotive. The woman says to the man: "Next time, order in English."
Paul said:
Condition 2 is the one that is necessary as a framework for the "voting strategy" discussions.
I reply:
Did you hear that, everyone? We�ve been wasting our time all these years :-)
Paul said:
I don't suggest that this is the only or best way to axiomatize the definition of "sincere preference", but as far as I know it's the first proposal that isn't ambiguous.
I reply:
You forgot to say what is ambiguous about how I most recently defined preference, in my posting whose subject line spoke of 4 approaches to preferece.
Mike Ossipoff
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