A Nonlinear, Nontransitive and Additive-Probability Model for Decisions Under Uncertainty

Let> denote a preference relation on a set F of lottery acts. Each f in F maps a state space S into a set P of lotteries on decision outcomes. The paper discusses axioms for > on F which imply the existence of an SSB (skew-symmetric bilinear) functional Phi on PxP and a finitely additive probability measure Pi on 2(S) such that, for all f and g in F,