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.
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Michael Taylor (1969) studied this question.
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