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The development of social choice theory over the past three decades has brought many new insights into democratic theory. Surprisingly, the theory of representation has gone almost untouched by social choice theorists. This article redresses this neglect and provides an axiomatic study of one means of implementing proportional representation. The distinguishing feature of proportional representation is its concern for the representativeness of deliberations as well as decisions. We define a representative in a way that is particularly attentive to this feature and then define a method of selecting representatives (a variant of the Borda rule) which selects a maximally representative body. We also prove that this method of selection meets four social choice axioms that are met by a number of other important social choice functions (including pairwise majority decision and the Borda rule).
Chamberlin et al. (Thu,) studied this question.