Believe and Let Believe: Axiomatic Foundations for Belief Dependent Utility Functionals

A large body of experimental data demonstrates that people's beliefs influence their well-being beyond the indirect effect through the actions taken. I present a model that incorporates beliefs into an agent's utility function. The paper provides axiomatic foundations for a special class of non-additive utility indices defined over infinite streams of beliefs and actions. I assume that: 1) there exists a (null) belief that does not have any effect on future preferences; 2) the agent has finite memory -- only finite histories have an effect on current preferences; and 3) if the agent knows she will not be getting any additional future information, she prefers today's beliefs to be consistent with her past choices. Preferences satisfying these assumptions admit a generalized discounted utility representation in which all terms depend on both actions and beliefs. Experimental testability of the proposed framework is also discussed.