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CARL WAGNER AVOIDING ANSCOMBE'S PARADOX 1. ANSCOMBE'S PARADOX As noted by Anscombe (1976), the disposition of a set of proposals by majority rule does not preclude the existence of a majority of voters, each of whom disagrees with the outcomes in a majority of cases. It is intuitively clear, however, that when proposals are adopted or rejected, on average, by a sufficiently strong consensus, such a state of affairs cannot materialize. Indeed, we show for N voters, K proposals, and 0< a,, B< 1, that when the prevailing coalitions', across all proposals, comprise on average at least (1-UO) N voters, the set of voters who disagree with more than aK outcomes cannot exceed, BN. Setting a= 3= 1/2, it follows that when prevailing coalitions comprise on average at least three-fourths of those voting, the set of voters disagreeing with a majority of outcomes cannot comprise a majority (see Wagner, 1983 …