## The Annals of Probability

### The Enumeration of Comparative Probability Relations

#### Abstract

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 $$O(3^{\alpha n^2})\quad \text{for} \log_2(3^{\frac{1}{2}}) \leqq \alpha \leqq 1.$$

#### Article information

Source
Ann. Probab. Volume 4, Number 4 (1976), 667-673.

Dates
First available: 19 April 2007

http://projecteuclid.org/euclid.aop/1176996036

JSTOR

Digital Object Identifier
doi:10.1214/aop/1176996036

Mathematical Reviews number (MathSciNet)
MR410820

Zentralblatt MATH identifier
0365.60005

Subjects
Primary: 60A05: Axioms; other general questions

#### Citation

Fine, Terrence; Gill, John. The Enumeration of Comparative Probability Relations. The Annals of Probability 4 (1976), no. 4, 667--673. doi:10.1214/aop/1176996036. http://projecteuclid.org/euclid.aop/1176996036.