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August, 1976 The Enumeration of Comparative Probability Relations
Terrence Fine, John Gill
Ann. Probab. 4(4): 667-673 (August, 1976). DOI: 10.1214/aop/1176996036


An attempt is made to enumerate the distinct antisymmetric comparative probability relations on sample spaces of $n$ atoms. The results include an upper bound to the total number of such relations and upper and lower bounds to the size of the subset of the comparative probability relations admitting an agreeing probability measure as representation. The theoretical results are supplemented by computer enumerations for $n \leqq 6$. The upper and lower bounds for the case of agreeing probability measures are both $$O(3^{\alpha n^2})\quad \text{for} \log_2(3^{\frac{1}{2}}) \leqq \alpha \leqq 1.$$


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Terrence Fine. John Gill. "The Enumeration of Comparative Probability Relations." Ann. Probab. 4 (4) 667 - 673, August, 1976.


Published: August, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0365.60005
MathSciNet: MR410820
Digital Object Identifier: 10.1214/aop/1176996036

Primary: 60A05

Keywords: Comparative probability , enumeration of orderings , qualitative probability

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 4 • August, 1976
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