[EM] cyclic preferences
atarr at purdue.edu
Thu Aug 5 08:21:33 PDT 2004
I will reiterate that allowing voters to cast cyclic ballots simply makes
the method more complicated and increases the chance of a spoiled
ballot. Even if I didn't oppose it on theoretical grounds, I would oppose
it on practical grounds. Onward...
Jobst Heitzig wrote:
>1. Consider a voter who evaluates the candidates according to a number
>of aspects (or dimensions, criteria, issues, perspectives, whatever).
>Assume that these aspects are not "measurable" in a numerical way but
>that s/he can only tell whether a candidate is better than another
>according to that aspect or not. Also, assume that s/he cannot assign
>priorities to those aspects but considers them equally important.
Cannot, or will not? Surely, with some thought, one can either attach
differing relative importance to certain positions on certain issues, or
can conclude that they are all equally important. One or the other has to
>further that for almost every pair X,Y of candidates there is an aspect
>in which X is better and another aspect in which Y is better. Most of
>you will agree that this situation is quite realistic, insn't it?
That part, sure.
> Now, what preferences shall the voter express in this situation?
>are two natural ways: S/he will express the preference X>Y if and only
>if X is better than Y according to either ALL aspects, or according to
>MOST aspects. The preference relations which can result from the first
>rule include all quasi-orders (= reflexive and transitive but not
>neccessarily total (="complete") relations), and those which can result
>from the second rule include all reflexive relations whatsoever, in
>particular, cyclic relations.
Again, I reject the idea that a rational voter could ever make a decision
simply by counting aspects/issues. It is trivial to take a position and
break it down into two sub-positions. For example: you could say that I
support legal abortions. Or, you could say I disagree with the notion that
a early-term fetus is an independent life, and that I believe that banning
abortions is impractical. Someone else may agree with both, neither, or
only one of those two aspects. But why should that breakdown make my
opinion twice as important?
> To give a concrete example: 3 candidates X,Y,Z, 3 aspects
> A1,A2,A3, and
>orderings X>Y>Z according to A1, Y>Z>X according to A2, Z>X>Y according
>to A3 (you all know this of course :-) The voter can either express no
>preference at all, or the cyclic preference X>Y>Z>X. Which gives us more
>information about his/her preferences? The latter, of course.
Not necessarily. If a voter truly feels that each issue has equal weight,
then X=Y=Z (voted above or below other candidates) is a completely
reasonable vote that tells us everything meaningful that voter has to
say. If the voter simply lacks the patience and rationality to resolve his
or her preferences into a transitive ordering, then in my opinion his or
her vote is just noise.
>2. Consider a voter who has children to care for who have no right to
>vote however. Don't you think it would be responsible of the voter to
>vote not only in his/her own interest but also in the interest of
>his/her children? If so, s/he faces essentially the same problem as
>society does: s/he has to accumulate preferences in some way. So when
>X>Y>Z for herself, Y>Z>X for her son and Z>X>Y for her daughter, the
>most responsible thing to vote would of course be X>Y>Z>X.
A clever argument, but this is actually a very inequitable way to reflect
the wishes of our children. Note that in winning votes, your vote
effectively gives each of the three of you half a vote. In margins, each
of you has effectively a full vote. Yet, if all of you agreed on X>Y>Z,
your voting power per person is just one third (in both margins and
WV). Why should a united house have less impact? Not fair at all.
If we really feel that people should cast votes for their children (or
felons, or foreigners, or Floridians, or people too lazy to vote for
themselves), then we should be giving them the vote directly, not messing
with our election methods to allow certain sorts of fractional voting.
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