Qualitative Models for Decision Under Uncertainty without the Commensurability Assumption

TL;DR

This paper develops a purely qualitative, ordinal framework for decision making under uncertainty that does not rely on the traditional commensurability of utility and uncertainty, expanding the theoretical landscape of decision models.

Contribution

It introduces a novel ordinal axiom for preferences over acts, characterizes the unique decision rule form, and explores transitive instances and relaxations of the axiom.

Findings

Unique qualitative decision rule identified

Transitive preference instances characterized

Relaxed axiom allows new decision rule family

Abstract

This paper investigates a purely qualitative version of Savage's theory for decision making under uncertainty. Until now, most representation theorems for preference over acts rely on a numerical representation of utility and uncertainty where utility and uncertainty are commensurate. Disrupting the tradition, we relax this assumption and introduce a purely ordinal axiom requiring that the Decision Maker (DM) preference between two acts only depends on the relative position of their consequences for each state. Within this qualitative framework, we determine the only possible form of the decision rule and investigate some instances compatible with the transitivity of the strict preference. Finally we propose a mild relaxation of our ordinality axiom, leaving room for a new family of qualitative decision rules compatible with transitivity.