We study the recently discovered phenomenon of existence of comparative probability orderings on finite sets that violate Fishburn hypothesis - 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< 7 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. |
Keywords
Comparative probability ordering, Discrete cone, Quadratic residue
Math Review Classification
Primary 60 A05, 05 B20
; Secondary 05 B30
Last Updated
29/10/2004
Length
14 pages
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