Is it Possible to Define Subjective Probabilities in Purely Behavioral Terms? A Comment on Epstein-Zhang (2001)

It is shown that well-behaved preference orderings may exhibit the Ellsberg paradox on the set of unambiguous events as defined by Epstein and Zhang (2001). Moreover, since such counterexamples can be constructed even when the set of unambiguous events is rich, EZ’s main representation result does not clarify satisfactorily when the proposed definition delivers probabilistic sophistication on unambiguous events. We conclude by conjecturing that these problems indicate the existence of inherent limitations of a strictly behavioral approach to identifying probabilistic beliefs in the presence of ambiguity, rather than deficiencies in EZ’s implementation of that approach. ∗E-mail: [email protected]. This research was undertaken during the author’s stay at the Institute for Advanced Study, Princeton; the support of the Andrew Mellon foundation is gratefully acknowledged. A first draft of the paper was circulated in 2004.