Before revision:  By leveraging on the notion of one-player Bayesian Correlated Equilibrium in Bergemann and Morris (  2016) , we provide a tractable characterisation of the sharp identified set and discuss inference under minimal assumptions on the amount of information processed by the decision maker and under no assumptions on the rule with which the decision maker resolves ties. Simulations reveal that the obtained bounds on the preference parameters can be tight in several settings of empirical interest .
After revision:  By leveraging on the notion of one-player Bayesian Correlated Equilibrium in Bergemann and Morris ( 2016) , we provide a tractable characterisation of the sharp identified set and discuss inference under minimal assumptions on the amount of information processed by the decision maker and under no assumptions on the information that voters have about the returns to voting. We find that the assumptions on the information environment can drive the interpretation of voter preferences. Counterfactual exercises quantify the consequences of imperfect information in politics .