A Bayesian approach to testing decision making axioms

Abstract

Theories of decision making are often formulated in terms of deterministic axioms, which do not account for stochastic variation that attends empirical data. This study presents a Bayesian inference framework for dealing with fallible data. The Bayesian framework provides readily applicable statistical procedures addressing typical inference questions that arise when algebraic axioms are tested against empirical data. The key idea of the Bayesian framework is to employ a prior distribution representing the parametric order constraints implied by a given axiom. Modern methods of Bayesian computation such as Markov chain Monte Carlo are used to estimate the posterior distribution, which provides the information that allows an axiom to be evaluated. Specifically, we adopt the Bayesian p -value as the criterion to assess the descriptive adequacy of a given model (axiom) and we use the deviance information criterion (DIC) to select among a set of candidate models. We illustrate the Bayesian framework by testing well-known axioms of decision making, including the axioms of monotonicity of joint receipt and stochastic transitivity.