On the Ellsberg and Machina paradoxes

This paper constructs a simple model of decision-making that accounts for the paradoxes of Ellsberg and Machina. It does so by representing decision makers’ beliefs on the vector space $${\mathbb{R}}\times {\mathbb{R}}$$ R × R and by providing a reasonable decision rule with axiomatic foundations. Moreover, the model allows for a characterization that clearly distinguishes between the two paradoxes. The interesting feature of the paper is that the ‘resolution’ of the paradoxes is along the lines suggested by the eponymous authors themselves. This is to say, the decision rule derived from the axioms corresponds to Ellsberg’s own rule in the narrow set of circumstances that he explored, and the decision rule embodies Machina’s injunction that we treat choice under uncertainty in a similar manner to the way we treat standard consumer theory. That the paper cleaves to the advice of both authors is a little surprising given that it utilizes a two-dimensional vector space that neither author deployed.