A Comparison of Axiomatic Approaches to Qualitative Decision Making Using Possibility Theory

TL;DR

This paper compares two axiomatic frameworks for qualitative decision making under possibility theory, unifying optimistic and pessimistic criteria through a simplified, ordered, binary utility approach.

Contribution

It introduces a unification of two axiomatic systems for qualitative decision making, simplifying and connecting optimistic and pessimistic criteria within possibility theory.

Findings

Unified axiomatic system for qualitative decision making

Representation of utilities with binary pairs

Simplified axiomatic framework

Abstract

In this paper we analyze two recent axiomatic approaches proposed by Dubois et al and by Giang and Shenoy to qualitative decision making where uncertainty is described by possibility theory. Both axiomtizations are inspired by von Neumann and Morgenstern's system of axioms for the case of probability theory. We show that our approach naturally unifies two axiomatic systems that correspond respectively to pessimistic and optimistic decision criteria proposed by Dubois et al. The simplifying unification is achieved by (i) replacing axioms that are supposed to reflect two informational attitudes (uncertainty aversion and uncertainty attraction) by an axiom that imposes order on set of standard lotteries and (ii) using a binary utility scale in which each utility level is represented by a pair of numbers.