A Qualitative Linear Utility Theory for Spohn's Theory of Epistemic Beliefs
This work addresses decision-making under qualitative uncertainty for researchers in AI and decision theory, but it appears incremental as it adapts existing axiomatic frameworks to a qualitative setting.
The paper tackles the problem of decision-making under qualitative uncertainty by formulating a qualitative linear utility theory based on Spohnian disbelief functions, showing that rational decision makers should maximize qualitative expected utility.
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.