On the Existence of Extremal Cones and Comparative Probability Orderings
نویسنده
چکیده
We study the recently discovered phenomenon [1] of existence of comparative probability orderings on finite sets that violate Fishburn hypothesis [2, 3] — we call such orderings and the discrete cones associated with them extremal. Conder and Slinko constructed an extremal discrete cone on the set of n = 7 elements and showed that no extremal cones exist on the set of n ≤ 6 elements. In this paper we construct an extremal cone on a finite set of prime cardinality p if p satisfies a certain number theoretical condition. This condition has been computationally checked to hold for 1,725 of the 1,842 primes between 132 and 16,000, hence for all these primes extremal cones exist.
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تاریخ انتشار 2005