  We study a Bayesian persuasion setting in which the receiver is trying to
match the (binary) state of the world. The sender's utility is partially
aligned with the receiver's, in that conditioned on the receiver's action, the
sender derives higher utility when the state of the world matches the action.
  Our focus is on whether, in such a setting, being constrained helps a
receiver. Intuitively, if the receiver can only take the sender's preferred
action with a smaller probability, the sender might have to reveal more
information, so that the receiver can take the action more specifically when
the sender prefers it. We show that with a binary state of the world, this
intuition indeed carries through: under very mild non-degeneracy conditions, a
more constrained receiver will always obtain (weakly) higher utility than a
less constrained one. Unfortunately, without additional assumptions, the result
does not hold when there are more than two states in the world, which we show
with an explicit example.
