[EM] Suppose, for a moment, there were never any cycles...
robert bristow-johnson
rbj at audioimagination.com
Sat Jan 21 11:49:02 PST 2023
So I am trying to grok this Benoit paper https://people.cs.pitt.edu/~kirk/CS1699Fall2014/gibbard-sat.pdf and I might be able to do it. But I would like to ask the authorities here a simple hypothetical question.
We know that Condorcet cycles can occur and in the U.S. there is one known RCV election that demonstrated a cycle, the 2021 Minneapolis Ward 2 City Council election. It was a simple Rock-Paper-Scissors cycle; Smith set of 3.
I think it's the case that we know that the necessary ingredients for a cycle is a very close 3-way race *and* that there is at least a 2-dimensional political spectrum (Nolan chart) with candidates and voters spread out all over the map in 2 dimensions, *not* in mostly a linear spatial distribution. There has to be a sorta political schizophrenia where a lotta voters are saying something like "If I can't have my favorite, Bernie, then I'm voting for T****."
Here is my question: Suppose that cycles *never* happened. Suppose we were somehow guaranteed that there is *always* a Condorcet winner. And also suppose we're far enough from a cycle that no collective strategy would succeed at pushing the election into a cycle. Then, *if* there is always a CW, is there any strategy that will serve a voter's political interest than better than ranking the candidates sincerely?
Like, if there is always a CW, how can IIA be violated? It seems to me that, if you remove *any* loser from all ballots and the voters express their same preferences with the remaining candidates, that the same CW will be elected. Without exception (other than a cycle).
Sorry to give you folks such a meatball question, but remember, I am an activist, not a trained and published scholar in psephology or social choice theory.
Thank you in advance.
robert
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r b-j . _ . _ . _ . _ rbj at audioimagination.com
"Imagination is more important than knowledge."
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