On the Ellsberg Paradox and its Extension by Machina: A Hyper-Bayesian Account

Abstract

This paper proposes a model of expected utility maximization which accounts for the Ellsberg paradox and Machina’s extension of it. In the model, decision makers use a ring of hypercomplex numbers, and they do so in order to decompose their beliefs into ‘ambiguous’ or ‘unambiguous’ parts – with unambiguous beliefs being defined on the reals, and ambiguous beliefs defined otherwise. Decision makers whose beliefs are formed on the ring and who maximize expected utility on it, are then shown to behave in ways that are predicted by the Ellsberg paradox and its extension by Machina. An axiomatic foundation for decision makers’ utility maximizing behaviour is provided. Additionally, decision makers’ beliefs are shown to be representable as real, vector-valued capacities.

Keywords: Ellsberg paradox, ambiguity aversion, hypercomplex numbers

JEL Classification: D80, D81