## The Annals of Probability

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

### 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

**Permanent link to this document**

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

**JSTOR**

links.jstor.org

**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

**Keywords**

Comparative probability qualitative probability enumeration of orderings

#### 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.