Ambiguity, data and preferences for information - A case-based approach

In this paper we suggest a behavioral approach to decision making under ambiguity based on the available information. A decision situation is characterized by a set of actions, a set of outcomes, and an information context represented by a data-set containing action-outcome pairs. Decision-makers express preferences over the choice of action in a particular information context. Data-sets containing a larger number of observations, while keeping the frequency of observations constant, are considered less ambiguous. We derive a representation of preferences, which separates utility and beliefs. While the utility function is purely subjective, the beliefs of the decision maker combine objective characteristics of the data (number and frequency of observations) with the subjectively perceived relevance of observations (similarity). We identify the subjectively perceived degree of ambiguity and separate it into ambiguity due to a limited number of observations and ambiguity due to data heterogeneity. We also determine the decision maker’s attitude towards ambiguity. The special case of no ambiguity represents beliefs as similarity-weighted frequencies. It provides a behavioral foundation for Billot, Gilboa, Samet and Schmeidler’s (2005) representation of the mapping from data sets to probabilites over outcomes. 1 We would like to thank to Larry Blume, Eric Danan, David Easley, Gaby Gayer, Itzhak Gilboa, John Hey, Edi Karni, David Kelsey, Nick Kiefer, Peter Klibanoff, Mark Machina, Francesca Molinari, Ben Polak, Karl Schlag, David Schmeidler, conference participants at RUD 2008 in Oxford, FUR 2008 in Barcelona and at the Workshop on Learning and Similarity 2008 in Alicante, as well as seminar participants at Cornell, UC Davis, Cergy Pontoise and George Washington University for helpful suggestions and comments. 3 University of Heidelberg, Alfred Weber Institute, Grabengasse 14, 69117 Heidelberg, Germany, e-mail: [email protected] 3 Corresponding author. University of Cergy, THEMA, 33 bd. du Port, 95011 Cergy Pontoise, France, e-mail: [email protected]