Some remarks on the probability of cycles - Appendix 3 to 'Epistemic democracy: generalizing the Condorcet jury theorem

This item was published as 'Appendix 3: An Implication of the k-option Condorcet jury mechanism for the probability of cycles' in List and Goodin (2001) Standard results suggest that the probability of cycles should increase as the number of options increases and also as the number of individuals increases. These results are, however, premised on a so-called "impartial culture" assumption: any logically possible preference ordering is assumed to be as likely to be held by an individual as any other. The present chapter shows, in the three-option case, that given suitably systematic, however slight, deviations from an impartial culture situation, the probability of a cycle converges either to zero (more typically) or to one (less typically) as the number of individuals increases.
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