Carlwagner Avoiding Anscombe's Paradox 1. Anscombe's Paradox
نویسنده
چکیده
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 < c~,/~ < 1, that when the prevailing coalitions ~, across all proposals, comprise on average at least (1 -t~/3)N voters, the set of voters who disagree with more than c~K outcomes cannot exceed /~N. Setting t~ = ~ = 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). Examples are provided to illustrate the "best possible" nature o f these and related results.
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