Mixing with and without randomness
ECONOMICS AND DECISION SCIENCES DEPARTMENT
Speaker : Paolo GHIRARDATO (Collegio Carlo Alberto-Turin)
HEC Campus- Building T - Room T017
We provide, and characterize behaviorally, two frameworks for identifying utility midpoints, and hence subjective mixtures, from preferences. The first one requires nontrivial uncertainty: It requires neither the Certainty Independence nor the Monotonicity axiom, replacing them with much weaker ``local'' properties. As we also show by means of examples, this framework provides a purely subjective foundation to most of the recent preference models which employ the Anscombe-Aumann setting.
The second framework builds on the assumption that payoffs are vectors and that preferences are additively separable. This construction of utility midpoints allows us to define mixtures of acts in a purely subjective fashion, without making any assumptions as to the decision maker's reaction to the uncertainty that may be present. This second framework makes it possible to provide a simple and fully subjective characterization of the second-order subjective expected utility model, and that it allows a clear distinction of such model from subjective expected utility.
Both frameworks allow a subjective formulation of a preference for ambiguity hedging, and as a consequence allows the distinction of the notions of ambiguity aversion and preference for randomization.