Qualitative Models for Decision Under Uncertainty without the Commensurability Assumption
This work addresses foundational issues in decision theory for researchers and practitioners by proposing a novel qualitative approach, though it appears incremental as it builds on existing Savage theory.
The paper tackles the problem of decision making under uncertainty by relaxing the commensurability assumption in Savage's theory, resulting in a purely qualitative framework that determines the only possible form of the decision rule and explores instances compatible with transitivity.
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.