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 $$O(3^{\alpha n^2})\quad \text{for} \log_2(3^{\frac{1}{2}}) \leqq \alpha \leqq 1.$$
Publié le : 1976-08-14
Classification:
Comparative probability,
qualitative probability,
enumeration of orderings,
60A05
@article{1176996036,
author = {Fine, Terrence and Gill, John},
title = {The Enumeration of Comparative Probability Relations},
journal = {Ann. Probab.},
volume = {4},
number = {6},
year = {1976},
pages = { 667-673},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996036}
}
Fine, Terrence; Gill, John. The Enumeration of Comparative Probability Relations. Ann. Probab., Tome 4 (1976) no. 6, pp. 667-673. http://gdmltest.u-ga.fr/item/1176996036/