Schedule - Parallel Session 6 - Axiomatic Foundations of Utility Theory

Economic decisions under uncertainty are often constrained by the restrictions imposed by their environment. For instance, consider a farmer who must make planting decisions without knowing the future temperature, rainfall, or sunshine. The outcomes of his various planting strategies, in terms of crop yields, are thus uncertain at the moment of choice. But furthermore, slight variations of the meteorological conditions will only result in slight variations in yields. Put differently, technological feasibility constraints impose continuous production plans: the farmer can only supply crop quantities that depend continuously on the meteorological conditions. Other examples where continuity with respect to uncertainty emerges as a technological constraint include the production of drinking water, hydroelectricity or solar power; the design of supply networks; the adoption of climate change policies or pollution abatement technologies. We study such situations of decision-making under uncertainty where feasibility constraints impose continuity restrictions on the available alternatives. More specifically, we provide an axiomatic treatment of Subjective Expected Utility (SEU) that is adapted to these situations. The uncertainty that affects a decision problem is given by a topological space of states of the world. The various possible consequences of decisions are given by a topological space of outcomes. Furthermore, we assume an exogenously given collection of continuous functions, or acts, from the state space onto the outcome space. This collection describes the set of all the theoretically conceivable alternatives that conform to the continuous technological constraints. The preferences of a decision-maker only rank these feasible acts. Thus, the classical Savage (1954) approach to SEU does not apply to such a restricted domain of acts. In this context, we identify a system of axioms on these preferences that characterize the existence and uniqueness of an SEU representation. In the representation, behavior is explained in terms of tastes and beliefs. Tastes take the form of a continuous utility function on the space of outcomes, thereby capturing the intuition that “similar outcomes” are assigned “similar utility levels”. Meanwhile, the specific form of beliefs depends on the topological assumptions made on the state space. For instance, if it is Hausdorff and compact, then beliefs are represented by a Borel probability measure. But, in general, beliefs take the form of what we call a credence. A credence on a topological state space is a finitely additive probability measure on a specific subdomain of the topology; namely, the Boolean algebra of regular events. Despite the restrictions we impose on both acts and events, we obtain an SEU representation where the utility function is unique up to positive affine transformation, and the credence (or Borel probability measure) is uniquely defined.