ARTICLE IN PRESS Journal of Economic Theory ( ) – www.elsevier.com/locate/jet Small worlds: Modeling attitudes toward sources of uncertainty Soo Hong Chew a , Jacob S. Sagi b, ∗ a Department of Economics, Hong Kong University of Science andTechnology, Hong Kong b Owen Graduate School of Business,Vanderbilt University, USA Received 26 June 2006; final version received 2 July 2007 Abstract We introduce the concept of a conditional small world event domain—an extension of Savage’s [The Foundations of Statistics, Wiley, NewYork, 1954] notion of a ‘small world’—as a self-contained collection of comparable events. Under weak behavioral conditions we demonstrate probabilistic sophistication in any small world event domain without relying on monotonicity or continuity. Probabilistic sophistication within, though not necessarily across, small worlds provides a foundation for modeling a decision maker that has source-dependent risk attitudes. This also helps formalize the idea of source preference and suggests an interpretation of ambiguity aversion, often associated with Ellsberg-type behavior, in terms of comparative risk aversion across small worlds. © 2007 Elsevier Inc. All rights reserved. JEL classification: D11; D81 Keywords: Uncertainty; Risk; Ambiguity; Decision theory; Non-expected utility; Utility representation; Probabilistic sophistication; Ellsberg paradox 1. Introduction In what has come to be known as Ellsberg’s [6] two-urn problem, a related version of which was proposed in Keynes [20], one urn contains 50 red and 50 black balls while the second contains an unspecified combination of the two. It is observed that individuals are indifferent to betting on a red ball versus a black ball from the same urn, and yet prefer to bet on a ball (of either color) from the urn with the known mixture. Such betting preferences are not consistent with ∗ Corresponding author. E-mail addresses: chew.sh@ust.hk (S.H. Chew), Jacob.Sagi@Owen.Vanderbilt.edu (J.S. Sagi). 0022-0531/$ - see front matter © 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.jet.2007.07.004 Please cite this article as: S.H. Chew, J.S. Sagi, Small worlds: Modeling attitudes toward sources of uncertainty Journal of Economic Theory (2007), doi: 10.1016/j.jet.2007.07.004