Jameson Quinn misinterpreted what I wrote. He claimed I described a random elections model. I described a scenario where 3 candidates are very similar, which is not the same as utter randomness.
Assuming the votes in all three pairings are very close to 50%--which would be expected if the 3 candidates are very similar--I think the chance of a majority cycle is nearly 25%, since there are 8 combinations of pairwise results, and 2 of the 8 are cyclic: [A>B, B>C, C>A] and [B>A, C>B, A>B]. (I should have worked that out before posting my previous message, which wrongly suggested the chance of a cycle would be nearly 50%.) Regards, Steve ----------------------------------------------- > 2009/12/9 seppley <[email protected]> wrote: >> Without studying details of the three Romanian candidates and the >> voters' >> preferences, the explanation of this majority cycle cannot be known for >> sure. >> >> However, consider a case of three very similar candidates. The voters' >> preferences in each of the three possible pairings would be nearly tied >> (approximately 50% preferring each candidate over each other candidate). >> In such a case, a cycle involving three small majorities would not be >> rare. Almost an even bet? Jameson Quinn wrote: > Not rare, you're right. However, what you are describing is essentially > something like a "random elections model" or perhaps a "Dirchlet model", > which, according to WDS's table of > calculations<http://rangevoting.org/Romania2009.html>, > for 3 or 4 serious candidates, have probabilities of Condorcet cycles > somewhere in the range of 6-18% - which is certainly nothing to be shocked > about when it happens by chance, but also a good deal less than an even > bet. > >> --Steve >> -------------------------- >> Jameson Quinn wrote: >> > This is good math, and very interesting, but it doesn't speak at all >> about >> > the politics of the matter. Have you figured out any tentative >> explanation >> > for the Condorcet cycles you postulate? Why would, for instance, O>B>G >> > voters be more common than O>G>B voters, yet in the mirror-image >> votes, >> > B>G>O voters more common than G>B>O ones? (I realize that the >> Condorcet >> > cycle does not require exactly that circumstance, but it suggests% ---- Election-Methods mailing list - see http://electorama.com/em for list info
