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).
Abstract We model the social planner's decision to establish universities and populate them with students and resources, given a distribution of student ability and a limited pool of resources for higher education. If student ability and school resources are complements, and if there is a fixed cost to establishing a school, then the optimal allocation will involve a tiered system of higher education that sorts students by ability. In contrast to previous research, we show this tiered system is optimal even in the absence of peer effects. In considering where to locate students, the planner balances the benefit of providing students with more resources against the congestion costs of overcrowding schools. Nearly identical students who are close to the margin of entry to a higher or lower tier will experience discrete gaps in education quality. In considering how many universities to establish, the planner will balance the value of more precise tailoring against the cost of establishing additional schools. The planner's inability to perfectly tailor education quality will result in both winners and losers. Our model also makes predictions about how university systems that serve different populations should vary. Larger systems will produce more per dollar of expenditures and more education per student, due to economies of scale.