[EM] Paul, 4 March, '05, 1450 GMT

[MIKE OSSIPOFF]

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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