Monotonicity in Condorcet Jury Theorem

Consider a committee of experts dealing with dichotomous choice problem, where the correctness probabilities are all greater than 1/2. We prove that, if a random subcommittee of odd size m is selected randomly, and entrusted to make a decision by majority vote, its probability of deciding correctly increases with m. This includes a result of Ben-Yashar and Paroush (2000), who proved that a random subcommittee of size m ≳ 3 is preferable to a random single expert.