Demand Aggregation and the Weak Axiom of Stochastic Revealed Preference

We address the problem of aggregating demand across a group of consumers, who are identical in terms of wealth and face identical price vectors, but vary in their chosen consumption bundles. We show that, when a stochastic demand function is constructed to aggregate a number of deterministic demand functions, satisfaction of the weak axiom of stochastic revealed preference by this stochastic demand function is weaker than the restriction that every underlying deterministic demand function satisfy Samuelson's weak axiom of revealed preference.