“Reverse Bayesianism”: A Choice-Based Theory of Growing Awareness

Abstract

This article introduces a new approach to modeling the expanding universe of decision makers in the wake of growing awareness, and invokes the axiomatic approach to model the evolution of decision makers' beliefs as awareness grows. The expanding universe is accompanied by extension of the set of acts, the preference relations over which are linked by a new axiom, invariant risk preferences, asserting that the ranking of lotteries is independent of the set of acts under consideration. The main results are representation theorems and rules for updating beliefs over expanding state spaces and events that have the flavor of "reverse Bayesianism." (JEL D81, D83)According to the Bayesian paradigm, as new discoveries are made and new information becomes available, the universe shrinks: with the arrival of new information, events replace the prior universal state space to become the posterior state space, or universe of discourse. This process of "destruction" reflects the impossibility, in the Bayesian framework, of expanding the state space and of updating the probabilities of null events, coupled with the fact that conditioning on new information renders null events that, a priori, were nonnull. Yet, experience and intuition alike contradict this view of the world. Becoming accustomed to possibilities that were once inconceivable is part of history and our own life experience. There is a sense, therefore, in which our universe expands as we become aware of new opportunities.In this paper we take a step toward modeling the process of growing awareness and expansion of the universe, or state space, in its wake. 1 To model the evolution of beliefs in response to growing awareness, we invoke the theory of choice under uncertainty; borrowing its language and structure while modifying it to fit our purpose. In particular, we allow for new consequences and feasible acts to be discovered and for new evidence to establish, in the mind of decision makers, new links between acts and consequences. The interpretation of the updating is somewhat different for the discovery of new feasible acts and consequences on the one hand 1 Dekel, Lipman, and Rustichini (1998) argue that standard state spaces preclude unawareness. A choice theoretic approach therefore needs a more general point of departure than Savage (1954) and Anscombe and Aumann (1963).

Managing Catastrophic Climate Risks Under Model Uncertainty Aversion

“…From a decision maker's perspective, becoming aware of such occurrences leads to the expansion of the set of admissible states of the world. Therefore, the state space and the associated probabilities need to be adjusted for making decisions when considering such "unforeseen events" (Karni and Viero 2013). In recent years, a few studies have been undertaken to estimate these probabilities, consisting generally of experts' assessments.…”

Extension Rules or What Would the Sage Do?

“…7 Ghirardato et al [4] prove this result when H = F; however, the same proof holds in general as well, even if the preferences over H are incomplete.…”

“…Related literature. Gilboa et al [5] and Karni and Vierø [7] are the most closely related papers to the current one. Unlike the primitive of our model, Gilboa et al [5] consider a pair of preference relations, Knightian and maxmin.…”

“…Karni and Vierø [7] consider a Bayesian agent and allow the set of alternatives to expand, that is, they let the agent become aware of new alternatives, outcomes and states of the world. Similarly to Gilboa et al [5], they assume the structure of the agent's preferences also in the post-expansion world.…”

“…7 It implies that if one wishes to employ the prudent rule in a consistent manner, one should apply it to the preferences' Knightian component.…”