Critique and comment: Proof of a theorem on majority rule

A mathematical proof is presented of a result due to Douglas Rae: simple majority rule is the unique decision rule (from among all possible decision rules, k = 1, 2, -, n in a committee of size n) which minimized the probability that a typical member will support a motion which the committee rejects or oppose a motion which is accepted, if he assumes that future preferences are unknown and that members vote (for or against) independently.