A nonlinear, nontransitive and additive-probability model for decisions under uncertainty
The authors investigate an extension of the classical Ramsey-Savage model of decision under risk as follows: Let p be a convex set of probability distributions on a set of outcomes and let F be the set of acts, i.e., of functions from a set S of states into P; \(\succ\) denotes a strict preference relation on F. The paper introduces and discusses axioms for \(\succ\) in the case of an infinite S which imply for f,g\(\in F\) that \(f\succ g\) if and only if \[ \int_{S}\phi (f(s),g(s)) d\pi (s)>0. \] Here \(\phi\) is an SSB (skew-symmetric bilinear) functional on \(P\times P\) and \(\pi\) a finitely-additive probability measure on \(2^ S\). The model which is called \(S^ 3B\) weakens the assumptions of transitivity and independence (compared to Ramsey and Savage) and preserves the classical probability structure.
scientific article; zbMATH DE number 4031349