Monopoly agenda control with privately informed voters

An agenda-setter repeatedly proposes a spatial policy to voters until some proposal is accepted. Voters have distinct but correlated preferences and receive private signals about the common state. I investigate whether the agenda-setter retains the power to screen voters as players become perfectly patient and private signals become perfectly precise. I show that the extent of this power depends on the relative precision of private signals and the conflict of preferences among voters, confirming the crucial role of committee setting and single-peaked preferences. When the private signals have equal precision, the agenda-setter can achieve the full-information benchmark. When one voter receives an asymptotically more precise signal, the agenda-setter's power to screen depends on preference diversity. These results imply that the lack of commitment to a single proposal can benefit the agenda-setter. Surprisingly, an increase in the voting threshold can allow the agenda-setter to extract more surplus.