The exchangeable multinomial model as an approach to testing deterministic axioms of choice and measurement

The multinomial (Dirichlet) model, derived from de Finetti's concept of exchangeability, is proposed as a general Bayesian framework to test axioms on data, in particular, deterministic axioms characterizing theories of choice or measurement. For testing, the proposed framework does not require a deterministic axiom to be cast in a probabilistic form (e.g., casting deterministic transitivity as weak stochastic transitivity). The generality of this framework is demonstrated through empirical tests of 16 different axioms, including transitivity, consequence monotonicity, segregation, additivity of joint receipt, stochastic dominance, coalescing, restricted branch independence, double cancellation, triple cancellation, and the Thomsen condition. The model generalizes many previously proposed methods of axiom testing under measurement error, is analytically tractable, and provides a Bayesian framework for the random relation approach to probabilistic measurement (J. Math. Psychol. 40 (1996) 219). A hierarchical and nonparametric generalization of the model is discussed.