Two-Sided Plausibility Constraints in Persuasion

A sender with commitment provides additional information to an already informed receiver. Final posterior means must be more dispersed than initial means and less dispersed than the state, in convex order. We characterize when these two plausibility constraints are also sufficient, so that every distribution satisfying them can be induced. If the state has a positive density, they are sufficient exactly under interval-partition information: the receiver learns which interval of a partition contains the state and nothing more, where an interval may be a single point. Otherwise, a nonempty open set of distributions satisfying both constraints cannot be induced, even when the sender observes the receiver's information. We use the sufficient case to derive an optimal symmetric disclosure rule in a second-price auction where bidders initially know valuation intervals.