Monotonicity in Condorcet Jury Theorem under Strategic Voting

The Condorcet jury theorem states that if members' voting probabilities for the better alternative are identical and independent among members, and larger than 1/2, then the probability that a committee under simple majority voting chooses the better alternative is monotonically increasing in the committee size. This implies that the committee under simple majority voting decides more efficiently than single-person decision-making. This superiority of group decision-making under strategic voting for the binary signal model has already been demonstrated. We generalize this result and prove that the monotonicity property in the Condorcet jury theorem holds in the symmetric efficient equilibrium.