On the Possibility of Faithfully Representative Committees

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Abstract
By faithful representation we mean the delegation of decision making to a relatively small committee that, using a weighted voting rule, will for each pair of alternatives make sincere choices identical to those that would be made by the society as a whole, and with the same vote margins. We show that for any society, no matter how large, faithful representation is possible by a committee with no more than m(m − 1)/2 members, where m is the number of alternatives. We also show that for any society, no matter how nonideological the bulk of its electorate, social preferences can be faithfully represented by a committee whose members all have singlepeaked or single-troughed preferences. Thus, all societies can be faithfully represented by a committee whose members see the world in unidimensional terms—that is, representatives can share a coherent ideological perspective even though the electorates they represent lack such a perspective. We further show that the usual mechanisms of proportional representation and the modified form of proportional representation recently proposed by Chamberlin and Courant (1983) do not guarantee faithful representation, and we discuss mechanisms that may provide faithful representation, even in a context in which new alternatives can arise.