[EM] Cycles and Stubborn (but rational) Voters

[Kevin Venzke]

Alex,

I hope I understood what you meant.  When you say that the three candidates
each have "well-defined stances on a variety of issues," I believe you're only
saying that to make it clear that the voters are rational in holding cyclic
preferences.

I have two thoughts.  For a candidate to become the CW, he needs to be able
to move on the spectrum.  But if it's not possible for the three candidates to
move, because there are only a few, well-defined positions that can be taken
on the issue(s), then it's hopeless.  A candidate needs to have some other
currency to offer.  He needs another dimension on the spectrum to allow him
to move towards the voter median.

Suppose the only issue is what sort of film to watch: drama, comedy, or documentary.
A candidate stands for each.  None of them can become the CW unless they can also
make an issue of what to eat afterwards, let's say, or who gets to sit next to whom,
or who will not be invited next time if they don't submit.

My other thought is to use Approval: Make every voter decide, secretly, with
the results revealed simultaneously, whether they insist on their favorite, or
insist against their least favorite.

But if there really are only three voters, this won't work either.  Roll dice, or 
introduce another issue (the reason we don't see many cyclic ties in legislatures).


Kevin Venzke
stepjak at yahoo.fr


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