FIRST INTERNATIONAL SYMPOSIUM ON
IMPRECISE PROBABILITIES AND THEIR APPLICATIONS

Ghent, Belgium
30 June - 2 July 1999

ELECTRONIC PROCEEDINGS

Paolo Ghirardato and Massimo Marinacci

An Outline of a Comparative Foundation to Ambiguity Aversion

Abstract

The theory of subjective expected utility (SEU) has been extended in many recent works, allowing ambiguity to matter for choice. However, a fully satisfactory and general notion of ambiguity aversion, analogous to risk aversion for SEU, is still missing. This outline summarizes the findings of a much longer work of ours [9]. There, using a new preference model which encompasses most of the recent literature, we provide such a definition by building on a comparative notion of ambiguity aversion. The development of the latter is not immediate, since it is necessary to distinguish between differences in ambiguity and risk attitude. The solution we offer is very general as it only requires a richness condition on the set of consequences. Employing the comparative notion, we call `ambiguity averse' a preference relation which is `more ambiguity averse' than a SEU preference with similar risk attitude. We show that ambiguity aversion in this sense has a simple characterization, especially for the specific models that are most popular in the literature. We then build on these ideas to provide a definition of unambiguous act and event. We show that for preferences which have a consistent ambiguity attitude, the sets of unambiguous acts and events have a simple and easily checked characterization. As an illustration, we consider the classical Ellsberg 3-color urn problem and find

Keywords. Ambiguity aversion, Choquet expected utility, multiple priors, lower probabilities, canonical preference relations

The paper is available in the following formats and sites:

Authors addresses:

Paolo Ghirardato

Division of H&SS
California Institute of Technology
Pasadena, CA 91125
USA

Massimo Marinacci

Dip.to di Scienze Economiche
Universita` di Bologna
P.za Scaravilli, 2
40126 Bologna
Italy

E-mail addresses:

Paolo Ghirardato paolo@hss.caltech.edu
Massimo Marinacci marinacc@economia.unibo.it

Related Web Sites

Paolo Ghirardato


[ back to the Proceedings of ISIPTA '99 home page 
Send any remarks to the following address: smc@decsai.ugr.es