Threshold models for comparative probability on finite sets

Let > be a comparative probability relation on the set B-S of all subsets of a finite state space S. This paper presents and discusses necessary and sufficient axioms for several threshold models of >, whose general representational form yields a probability measure P on B-S and a bivariate set function Ohm greater than or equal to O on B-S x B-S such that for all A, B is an element of B-S, A > B if and only if P(A) > P(B) + Ohm(A, B). Several conditions such as skew-monotonicity and additive separability will be imposed on the functional form of Ohm. (C) 2000 Academic Press.