Eliaz (2004) has established a "meta-theorem" for preference aggregation which implies both Arrow's Theorem (1963) and the Gibbard-Satterthwaite Theorem (1973, 1975). This theorem shows that the driving force behind impossibility theorems in preference aggregation is the mutual exclusiveness of...

Many procedures have been suggested for the venerable problem of dividing a set of indivisible items between two players. We propose a new algorithm (AL), related to one proposed by Brams and Taylor (BT), which requires only that the players strictly rank items from best to worst. Unlike BT, in...

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...

This paper considers cost sharing rules for the continuous knapsack problem. We assume a knapsack with a weight constraint to be filled with items of different weights chosen from a set of items. The cost of the knapsack needs to be shared among the individuals who approve or disapprove of...

In this paper we investigate the problem of selecting a committee consisting of k members from a list of m candidates. Each candidate has a certain cost or weight. The choice of the k-committee has to satisfy some budget or weight constraint: the sum of the weights of all committee members must...

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...

An allocation of indivisible items among n ≥ 2 players is proportional if and only if each player receives a proportional subset—one that it thinks is worth at least 1/n of the total value of all the items. We show that a proportional allocation exists if and only if there is an allocation...