In this paper we show how theorems of Borsuk-Ulam and Tucker can be used to construct a consensus-halving: a division of an object into two portions so that each of n people believe the portions are equally split. Moreover, the division takes at most n cuts, which is best possible. This extends...

In this paper we show how theorems of Borsuk-Ulam and Tucker can be used to construct a consensus-halving: a division of an object into two portions so that each of n people believe the portions are equally split. Moreover, the division takes at most n cuts, which is best possible. This extends...

A cake is a metaphor for a heterogeneous, divisible good, such as land. A perfect division of cake is efficient (also called Pareto-optimal), envy-free, and equitable. We give an example of a cake in which it is impossible to divide it among three players such that these three properties are...

A cake is a metaphor for a heterogeneous, divisible good. When two players divide such a good, there is always a perfect division—one that is efficient (Pareto-optimal), envy-free, and equitable—which can be effected with a finite number of cuts under certain mild conditions; this is not...

We analyze a simple sequential algorithm (SA) for allocating indivisible items that are strictly ranked by n ≥ 2 players. It yields at least one Pareto-optimal allocation which, when n = 2, is envy-free unless no envy-free allocation exists. However, an SA allocation may not be maximin or...

A cake is a metaphor for a heterogeneous, divisible good. When two players divide such a good, there is always a perfect division — one that is efficient (Pareto-optimal), envy-free, and equitable — which can be effected with a finite number of cuts under certain mild conditions; this is not...

We apply a fallback model of coalition formation to decisions of the U.S. Supreme Court, focusing on the seven natural courts, which had the same members for at least two terms, between 1969 and 2009. The predictions of majority coalitions on each of the courts are generally bourn out by the 5-4...

This paper identifies the optimal options of Krabi's coastal land use to facilitate the final planning decision. Through compromise programming approach, the optimization models with respect to the weights assigned to two objectives of maximizing the net private and environmental benefits are...

This paper explores the tradeoff options for optimal coastal land use in Krabi's coastal land development zone (CLDZ). Maximizing the net private benefit and maximizing the net environmental benefits, subject to the constraints set by land availability, effluent discharge from shrimp farms, and...

Political instability of several countries in the Middle East is overshadowing one of the biggest challenges of the upcoming century: Water - a natural resource that is easily taken for granted, but whose scarcity might lead to serious conflicts. This paper investigates an optimal Water...