There are many real-world examples where decisions are made by a committee rather than all of the members of a court, legislature, or other body. The members of such committees are usually chosen either using random selection or using direct selection by a designated authority. However, neither...

A minimum cost spanning tree problem analyzes the way to efficiently connect agents to a source when they are located at different places. Once the efficient tree is obtained, the total cost should be allocated among the involved agents in a fair and stable manner. It is well known that there...

A new voting rule for electing committees is described. Specifically, we use approval balloting and propose a voting procedure guaranteeing that if a committee representing (in a determined proportion) all voters exists, then the selected committee has to represent all voters at least in the...

In this paper we consider convex combinations of matrices that arise in the study of distribution problems and analyse the properties of Perron's eigenvalue, and its associated positive eigenvector. We prove that the components in the (normalized) associated positive eigenvector have a monotone...

If we analyze the notion of stability (von Neumann and Morgenstern, 1944) it seems a desirable property to be fulfilled by any choice function. Paradoxically, the usual Condorcet choice functions (maximal set, top cycle, uncovered set, minimal covering, ...) are not stable in the VNM sense. In...

In 1950, Nash's seminal paper introduced the axiomatic approach to the analysis of bargaining situations. Since then, many bargaining solutions have appeared and been axiomatically analyzed. The fact that agents, when face a bargaining problem, can come up with different solution concepts (that...

We consider a cost sharing problem, where each individual is identi ed by a characteristic (a positive real number) ci: The two main positions on how to share a common cost M are the Egalitarian and the Proportional solutions. These solutions can be obtained as the Perron's eigenvectors (right...

The notion of a stable set (introduced by von Neumann and Morgenstern, 1944) is an important tool in the field of Decision Theory. Since then, some alternative definitions have appeared in the literature: the admissible set (Kalai and Schmeidler, 1977), the generalized stable set (van Deemen,...

The problem of sharing a cost M among n individuals, identified by some characteristic ci∈R+, appears in many real situations. Two important proposals on how to share the cost are the egalitarian and the proportional solutions. In different situations a combination of both distributions...

The notion of a stable set (introduced by von Neumann and Morgenstern, 1944) is an important tool in the field of Decision Theory. However, unfortunately, the stable set has some disadvantages: it is not unique, it may select too many alternatives and, most importantly, it may fail to exist....