A Stronger Case for Transitive Preferences

The assumption that preferences are transitive, or, equivalently, that choice behavior satisfies the Weak Axiom of Revealed Preference, is at the core of most economic theory. While this is a natural assumption, one could ask the degree to which it is restrictive: are there objectives that could not be attained by such behavior that could be attained by choices violating the assumption? It is argued that the answer to this question is no in one setting of choice under random budget sets.