Random choice with framing effects: a Bayesian model

I consider decision makers who experience framing effects facing different choice problems, such that the resulting random choice is incompatible with a single random utility model. I study conditions under which these framing effects could be exhibited by a population of expected utility maximizing (“Bayesian”) agents uncertain about their own tastes. The model assumes that framing of a choice problem is associated with a Blackwell experiment defined on the subjective state space of decision maker. The paper provides a characterization of this model in terms of one axiom on the observed random choice. If all choice probabilities are positive, Bayesian model allows for arbitrary framing effects, and I show that in general we need two additional components to discipline it. Firstly, analyst should have an ability to observe choice from different menus with the same framing, otherwise any random choice is rational for some agent who is uncertain about only two states of the world (for example, whether she is brave or not). Secondly, we should restrict a degree of preference variation for each decision maker, and Bayesian model provides a good way to do this implicitly by limiting the size of the subjective state space. Without the second restriction arbitrary framing effects could be justified even if analyst observes choice probabilities from all possible menus under each frame. This negative result holds even with strong structural assumptions on the informational part of the model, covering dynamic random choice and other applications. Finally, I provide examples showing that Bayesian models having both additional components do produce moderate framing effects, and I derive a sufficient condition on the size of the state space as a function of the number of alternatives for which moderate rather than arbitrary framing effects emerge.