This paper studies collective choice by participants possessing private information about the consequences of policy decisions in policymaking institutions that involve cheap-talk communication and bargaining. The main result establishes a connection between the extent to which problems of this type posses fully-revealing equilibria that select policies in the full information majority rule core (when it is well-defined) and the extent to which a fictitious sender-receiver game possesses a fully revealing equilibria. This result allows us to extend Banks and Duggan's (2000) core equivalence results to the case of noisy policymaking environments with private information when some combination of nonexclusivity and preference alignment conditions are satisfied.
