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according to the nlab entry on the Condorcet Paradox in social choice (that is voting preferences may be circular even if voters preferences are not) has a cohomological explanation - what is it?

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I think that there is nothing serious - Ghist only noticed the existence of cycles in the set of voted alternatives. If you are interested in algebraic methods of the theory of voting, I advise you to see the results of V.Danilov (e.g., http://arxiv.org/pdf/1011.2888.pdf and previous papers).

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