Theory and Decision

, Volume 46, Issue 2, pp 107-138

First online:

E-Capacities and the Ellsberg Paradox

  • Jürgen EichbergerAffiliated withWirtschaftstheorie, Universität des Saarlandes
  • , David KelseyAffiliated withDepartment of Economics, The University of Birmingham

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Ellsberg's (1961) famous paradox shows that decision-makers give events with ‘known’ probabilities a higher weight in their outcome evaluation. In the same article, Ellsberg suggests a preference representation which has intuitive appeal but lacks an axiomatic foundation. Schmeidler (1989) and Gilboa (1987) provide an axiomatisation for expected utility with non-additive probabilities. This paper introduces E-capacities as a representation of beliefs which incorporates objective information about the probability of events. It can be shown that the Choquet integral of an E-capacity is the Ellsberg representation. The paper further explores properties of this representation of beliefs and provides an axiomatisation for them.

Ellsberg paradox Uncertainty aversion Choquet integral Non-additive probabilities