A general revealed preference theorem for stochastic demand behavior

We present a general revealed preference theorem concerning stochastic choice behavior by consumers. We show that, when the consumer spends her entire wealth, the Weak Axiom of Stochastic Revealed Preference due to Bandyopadhyay, Dasgupta, and Pattanaik (1999) is equivalent to a restriction on stochastic demand behavior that we call stochastic substitutability. We also show that the relationship between the Weak Axiom of Revealed Preference and Samuelson's inequality in the deterministic theory, and the main result of Bandyopadhyay, Dasgupta, and Pattanaik (1999) are both special cases of our result.