CHOICES, CONSEQUENCES, AND RATIONALITY
ABSTRACT. A generalized theory of revealed preference is formulated for choice
situations where the consequences of choices from given menus are uncertain. In a non-
probabilistic framework, rational choice behavior can be deﬁned by requiring the existence
of a preference relation on the set of possible consequences and an extension rule for this
relation to the power set of the set of consequences such that the chosen sets of possible
outcomes are the best elements in the feasible set according to this extension rule. Rational
choice is characterized under various assumptions on these relations.
The analysis of rational choice behavior in economic models dates back as
far as Samuelson’s (1938) seminal contribution. Authors such as Samuel-
son (1938, 1948), Houthakker (1950), Uzawa (1960, 1971), Hurwicz and
Richter (1971), among others, develop the theory of revealed preference in
the context of consumer choice models. The goal of revealed preference
theory is to determine whether a given demand function can be generated
from a preference relation in the sense that, for each possible budget set,
the demanded commodity bundle is the best element in this set according
to this preference relation. Samuelson (1938, 1948) shows that the weak
axiom of revealed preference is necessary for rational choice. The strong
axiom of revealed preference – a necessary and sufﬁcient condition – is
introduced in Houthakker (1950). Uzawa (1960, 1971) derives rational-
izability from the weak axiom of revealed preference and a regularity
condition (see also Bossert (1993)). Rose (1958) shows that the weak
and strong axioms are equivalent if there are only two commodities (see
Blackorby, Bossert and Donaldson (1995) for a generalization to multi-
valued demands). For more than two commodities, this is not the case –
see Gale (1960), Kihlstrom, Mas-Colell, and Sonnenschein (1976), and
Peters and Wakker (1994). Furthermore, if a larger domain than the class
of budget sets is considered, this equivalence result does not necessarily
remain valid unless additional conditions are imposed. See, for example,
Peters and Wakker (1991) and Bossert (1994).
Synthese 129: 343–369, 2001.
© 2001 Kluwer Academic Publishers. Printed in the Netherlands.