A nonlinear, nontransitive and additive-probability model for decisions under uncertainty
type: Item
instance of: scholarly article
title: A nonlinear, nontransitive and additive-probability model for decisions under uncertainty
zbMATH Open document ID: 0633.90002
author: Peter Fishburn
author: Irving H. La Valle
published in: The Annals of Statistics
publication date: 1987-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 91B06
Mathematics Subject Classification ID: 91B16
zbMATH DE Number: 4031349
zbMATH Keywords: subjective expected utility
zbMATH Keywords: nontransitive preferences
zbMATH Keywords: Ramsey-Savage model
zbMATH Keywords: decision under risk
zbMATH Keywords: skew-symmetric bilinear
zbMATH Keywords: transitivity
zbMATH Keywords: independence
reviewed by: Karl Mosler
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176350378
OpenAlex ID: W2047955873
DOI: 10.1214/AOS/1176350378
description: scientific article; zbMATH DE number 4031349