Threshold Models for Comparative Probability on Finite Sets.
Let succeeds be a comparative probability relation on the set &Bscr;(S) of all subsets of a finite state space S. This paper presents and discusses necessary and sufficient axioms for several threshold models of succeeds, whose general representational form yields a probability measure P on &Bscr;(S) and a bivariate set function Omega>/=0 on &Bscr;(S)x&Bscr;(S) such that for all A, Bin&Bscr;(S), A succeedsB if and only if P(A)>P(B)+Omega(A, B). Several conditions such as skew-monotonicity and additive separability will be imposed on the functional form of Omega. Copyright 2000 Academic Press.
Nakamura
Y
University of Tsukuba, Tsukuba, Japan