, Volume 1, Issue 2, pp 139-144

An interpretation of Ellsberg’s Paradox based on information and incompleteness

Abstract

This note relates ambiguity aversion and private information, by offering an interpretation of the Ellsberg’s paradox in terms of incompleteness of preferences. We adopt the standard model of information in terms of a $\sigma $ -algebra $\Sigma $ of events. These events are the events that the decision maker is informed about and therefore able to judge its likelihood by attaching a probability value to them. Note that the decision maker is unable to compare acts that are not measurable with respect to $\Sigma $ , because those cannot be integrated using the standard expected utility framework. Her preferences are, therefore, incomplete. Facing a decision problem that requires comparing non-measurable acts, the decision maker is confronted with the problem of completing her preferences. Some natural ways of completing the preferences lead to the behavior described by the Ellsberg’s thought experiment.