A Subjective Foundation of Objective Probability∗

De Finetti’s concept of exchangeability provides a way to formal-ize the intuitive idea of similarity and its role as guide in decision making. His classic representation theorem states that exchangeable expected utility preferences can be expressed in terms of a subjec-tive beliefs on parameters. De Finetti’s representation is inextricably linked to expected utility as it simultaneously identifies the parameters and Bayesian beliefs about them. This paper studies the implications of exchangeability assuming that preferences are monotone, transitive and continuous, but otherwise incomplete and/or fail probabilistic so-phistication. The central tool in our analysis is a new subjective ergodic theorem which takes as primitive preferences, rather than probabili-ties (as in standard ergodic theory). Using this theorem, we identify the i.i.d. parametrization as sufficient for all preferences in our class. A special case of the result is de Finetti’s classic representation. W