# [EM] cyclic preferences

James Green-Armytage jarmyta at antioch-college.edu
Thu Aug 5 15:04:41 PDT 2004

```Jobst Heitzig, you wrote:
>	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.

What kind of information does it actually give us? Can you definitively
say that in an election only between Z and X, your voter would vote for Z,
and so on with all of the other pairs? I don't think so. So X>Y>Z>X isn't
really meaningful.

you 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.

Yes, but if A1: X>Y>Z, your voter prefers X to Z more strongly than he
prefers X to Y or Y to Z. Filling in cardinal numbers can help us
conceptualize this. If the voter can't muster any more meaningful
information beyond the fact that he likes X>Y>Z on issue A1, then we can
assume default ratings on A1 like so: X 100 > Y 50 > Z 0. If the voter
decides that Y's position is closer to Z's (bad) than X's (good), then he
can change the entry "Y 50" accordingly. So now we can look at the
individual comparisons. Here's the comparison between X and Y:

X vs. Y
A1: X>Y +50
A2: Y>X +100
A3: X>Y +50

So, comparing X to Y, we note that X beats Y on two of the issues, while
Y beats X on only one. If you stop here and count this as a victory for X,
then yes, you will get X>Y, Y>Z, Z>X, a cyclic preference. However, this
fails to take into account that the Y>X gap on issue A2 may be stronger
than the X>Y gaps on issues A1 and A3. Again, if you have more to say
beyond the 100-50-0 default ratings, then by all means say it. But in this
case it looks like two single gaps against one double gap. I think that,
in the absence of further information, X vs. Y is a tie. The rest of the
individual comparisons work the same way as this one. So I would indeed
say that your voter's preferences are best expressed as X=Y=Z.

you wrote:
>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.

>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.