Case-Based Expected Utility: Preferences over Actions and Data

We consider a decision-situation in which the available information is given by a data-set. The decision-maker can express preferences over data-set-action pairs. In particular, he can compare different actions given the available information contained in a data-set and also different data-sets w.r.t. to the evidence they give in support of the choice of a given action. Three characteristics of a data-set can be used to evaluate the evidence it provides with respect to the payoff of a given action: the frequency of observations, the number of observations and the relevance of observations to the action under consideration. We state axioms, which ensure that the decision maker is indifferent among data-sets with identical frequencies, but different lengths. We then provide an expected utility representation of preferences, in which the beliefs of the decision maker about the outcome of a given action can be expressed as similarity-weighted frequencies of observed cases, as in BGSS (2005). The similarity weights reflect the subjectively perceived relevance of observations for the specific action.