Qualitative decision rules under uncertainty

Abstract

This paper is a survey of qualitative decision theory focused on the available decision rules under uncertainty, and their properties. It is pointed out that two main approaches exist according to whether degrees of uncertainty and degrees of utility are commensurate (that is, belong to a unique scale) or not. Savage-like axiomatics for both approaches are surveyed. In such a framework, acts are functions from states to results, and decision rules are used to characterize a preference relation on acts. It is shown that the emerging uncertainty theory in qualitative settings is possibility theory rather than probability theory. However these approaches lead to criteria that are either little decisive due to incomparabilities, or too adventurous because focusing on the most plausible states, or yet lacking discrimination because or the coarseness of the value scale. Some new results overcoming these defects are reviewed. Interestingly, they lead to genuine qualitative counterparts to expected utility.