Agent Rationality Under Partially Resolving Uncertainty and the Hurwicz Criterion

The subjective expected utility theory (SEUT) due to Savage is a classical normative approach to represent agent’s preferences on random monetary amounts. A basic assumption behind SEUT is that the agent acts under completely resolving uncertainty, i.e., he/she will always acquire the information about the “true” state of the world. As advocated by Jaffray, some relevant decision conditions configure partially resolving uncertainty, according to which the agent could only acquire the truth of a non-elementary event, without knowing the “true” state of the world in it. When a non-elementary piece of information is learned, a gamble gives rise to several values and many selection criteria can be taken. As an example, the Hurwicz criterion chooses an average between the “best” and the “worst” result, according to a fixed pessimism index. Here, we consider preferences on gambles of an agent acting under partially resolving uncertainty, which has a linear utility scale and adopts the Hurwicz criterion. We propose a Dutch book rationality condition that assures the numeric representation of preferences, through a suitable Choquet expectation with respect to a subjective pair of dual belief and plausibility functions expressing a so-called α-DS mixture.