Fuzzy orderings with reference to an underlying context of similarity were first defined by Höhle and Blanchard [9]. Since then, several authors have contributed to the development of this class of fuzzy relations, both from the theoretical and the practical side (e.g. [1–4, 7, 8]). Two problems remained open throughout several years: how to define strict fuzzy orderings and how to define lexic...

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...