A Qualitative Linear Utility Theory for Spohn's Theory of Epistemic Beliefs

TL;DR

This paper develops a qualitative linear utility theory for decision making under uncertainty expressed through Spohn's disbelief functions, extending classical utility theory to qualitative beliefs.

Contribution

It introduces a new axiomatization of qualitative utility based on Spohnian disbelief, bridging qualitative beliefs and decision theory.

Findings

Formulates a qualitative expected utility maximization principle

Provides axioms similar to von Neumann-Morgenstern for qualitative beliefs

Compares with other qualitative decision-making frameworks

Abstract

In this paper, we formulate a qualitative "linear" utility theory for lotteries in which uncertainty is expressed qualitatively using a Spohnian disbelief function. We argue that a rational decision maker facing an uncertain decision problem in which the uncertainty is expressed qualitatively should behave so as to maximize "qualitative expected utility." Our axiomatization of the qualitative utility is similar to the axiomatization developed by von Neumann and Morgenstern for probabilistic lotteries. We compare our results with other recent results in qualitative decision making.