Given positive integers d and n, there is an integer N such that for every injective map ffrom { 1 ..... N} a into R there is a subset A = A1 x A2 x ... × Ad of { 1 ..... N} a such that (1) each Aj has n elements, (2) the restriction of f to A is monotone in each coordinate, (3) there is an ordering of the coordinates such that f on A is texicographic with respect to that ordering. Because inje...

T he 2008 annual Math Awareness Month theme features the unusual combination of “Mathematics and Voting”. The importance of voting is obvious; indeed, with the United States election season hard upon us, discussions about voting are seemingly nonstop. More generally, on almost any day of any year the news media reports on some consequential election going on somewhere in the world. But what doe...

The finding that the preferences of middle-income Americans are ignored when they diverge from the preferences of the rich is one of the most widely accepted and influential conclusions in political science research today. I offer a cautionary note regarding this conclusion. I demonstrate that even on those issues for which the preferences of the wealthy and those in the middle diverge, policy ...

Empirical studies of the connection between citizen preferences and legislator actions have largely focused on the preferences of a district’s average or median voter. While many theories suggest that preference heterogeneity should also affect this connection, few empirical analyses have rigorously tested claims about the distribution of individual voter preferences. In this paper, we use a un...

We present a simple and natural non-pricing mechanism for allocating divisible goods among strategic agents having lexicographic preferences. Our mechanism has favorable properties of strategy-proofness (incentive compatibility). In addition (and even when extended to the case of Leontief bundles) it enjoys Pareto efficiency, envy-freeness, and time efficiency. 1998 ACM Subject Classification F...

This paper characterizes lexicographic preferences over alternatives that are identified by a finite number of attributes. Our characterization is based on two key concepts: weaker notion continuity called “mild continuity” (strict preference order between any different with respect to every attribute preserved around their small neighborhoods) and an “unhappy set” (any alternative outside such...

We generalize the main result of [K–K–S] concerning the convex embeddings of a chain Γ in a lexicographic power ∆Γ. For a fixed non-empty chain ∆, we derive necessary and sufficient conditions for the existence of non-empty solutions Γ to each of the lexicographic functorial equations (∆) ' Γ , (∆) ' Γ and (∆) ' Γ .