On the Likelihood of Cyclic Comparisons

We investigate the procedure of "random sampling" where the alternatives are random variables. When comparing any two alternatives, the decision maker samples each of the alternatives once and ranks them according to the comparison between the two realizations. Our main result is that when applied to three alternatives, the procedure yields a cycle with a probability bounded above by 8 27 . Bounds are also obtained for other related procedures
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Steven Orla Kimbrough (1980). On the Use of Likelihood as a Guide to Truth. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:117 - 128.

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