Testing Single Crossing Property with Stochastic Choice Data

In a typical model of private information and choice under uncertainty, a decision maker observes a signal, updates her prior beliefs using Bayes rule, and maximizes her expected utility. If the decision maker's utility function satisfies the single crossing property, and the information structure is ordered according to the monotone likelihood ratio, then the comparative statics exhibit monotonicity with respect to signals. We consider the restrictions placed by this model of signal processing on state conditional stochastic choice data. In particular, we show that this model rationalizes a state conditional stochastic choice dataset if and only if the dataset itself is ordered according to the monotone likelihood ratio. A straightforward application of the main result shows the conditions under which the analyst can infer when one DM is more informed than the other.