We study path-independent choice rules applied to a matching context. We use a classic representation of these choice rules to introduce a powerful technique for matching theory. Using this technique, we provide a deferred acceptance algorithm for many-to-many matching markets with contracts and...

We introduce the first family of district compactness measures that can incorporate a wide range of internal geographic features. The measures in this family are the probability that a district contains an admissible path between a randomly selected pair of people. The measure can account for...

We introduce a new class of measures of scholarly influence, which we term step-based indices. This class includes the prominent h-index, the publication count, and the i10-index. We show that the class of step-based indices is characterized by three axioms, consistency with worse scientists,...

We investigate the results of Kreps (1979), dropping his completeness axiom. As an added generalization, we work on arbitrary lattices, rather than a lattice of sets. We show that one of the properties of Kreps is intimately tied with representation via a closure operator. That is, a preference...

We introduce an ordinal model of efficiency measurement. Our primitive is a notion of e ciency that is comparative, but not cardinal or absolute. In this framework, we postulate axioms that we believe an ordinal efficiency measure should satisfy. Primary among these are choice consistency and...

We introduce a path-based measure of convexity to be used in assessing the compactness of legislative districts. Our measure is the probability that a district contains the shortest path between a randomly selected pair of its points. The measure is defined relative to exogenous political...

We present a model of information aggregation in which agents' information is represented through partitions over states of the world. We discuss three axioms, meet separability, upper unanimity, and non-imposition, and show that these three axioms characterize the class of oligarchic rules,...