[EM] Re: Election-methods Digest, Vol 3, Issue 14
alex_small2002 at yahoo.com
Mon Sep 6 11:51:31 PDT 2004
This discussion of transitive preferences brings 3 thoughts to mind:
1) While one could complain that disallowing cyclic preferences unnecessarily restricts a voter's freedom of choice, somebody else could complain that using ordinal preferences instead of cardinal ratings restricts freedom of expression. A voting method has to impose some type of simplification on the information that a voter presents.
2) I will agree that in some cases I might prefer A to B, in others I might prefer B to C, and in others I might prefer C to A. However....
Such intransitive preferences will be most likely to occur for me if there is no third choice present at the time (i.e. each preference is given at different times) AND if the terms of the debate are different each time.
For instance, if A and B are the only candidates in the race then the issues debated will be different. In light of the information presented IN THAT PARTICULAR CONTEST, I might prefer A to B. If B and C were in the race, AND DIFFERENT INFORMATION WERE PRESENTED TO ME, I might prefer B to C. And, finally, if C and A were in a contest, AND DIFFERENT INFORMATION WERE PRESENTED TO ME, I might prefer C to A in light of that information.
However, if I'm evaluating all 3 candidates against the same data set, I have a harder time seeing how I'd get cyclic preferences as an individual.
3) A fun story: I once tried to use cyclic preferences as an excuse to goof off, but I couldn't quite bring myself to do it. In my first year of grad school I had 3 options for a particular Saturday: Spend the day in the cleanroom doing a group project for a class, spend the day at a quasi-mandatory departmental orientation for first year students, or spend the day at a Graduate Student Association hike, meeting students from outside science and engineering, i.e. female students (I was single back then).
I wanted to procrastinate the project, so going to a quasi-mandatory orientation with free food seemed preferable (and a valid excuse to give my collaborators). However, going hiking seemed more fun than the orientation. Finally, in a comparison between hiking and the project, I didn't know if I could justify hiking to my project collaborators.
Notice that in each case I considered a different issue (procrastination, women, and responsibility). I finally broke the cycle by deciding that if I was going to skip out on my collaborators it should be for something at least somewhat responsible instead of hiking, so I went to the orientation with free food.
Date: Mon, 06 Sep 2004 13:06:09 -0500
From: Adam Tarr
Subject: Re: [EM] Cycles in sincere individual preferences and
application to vote-collection
Message-ID: <220.127.116.11.0.20040906124955.0371bb78 at min.ecn.purdue.edu>
Content-Type: text/plain; charset="us-ascii"
And therein lies my objection. I don't think you can simply substitute
individual for group. A group can have cyclic preferences, and on that
fact rests Condorcet's paradox and Arrow's theorem.
But I do NOT believe that an individual can have such preferences. Or,
more accurately, an individual may have such preferences, but I do not
consider them logical, and I have absolutely no interest in factoring such
preferences into a social choice algorithm.
I guess this makes me a "transitive preference elitist" of sorts. I'm
comfortable with that.
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