A problem in Social choice

R. Lucchetti, G. Bernardi, S. Moretti

Suppose to face the problem to rank individuals on the basis of their performances when acting within groups. How is it possible to do in a fair way? Of course, how to do it depends on the underlying assumptions one wants to consider. However, a typical approach in this area is the following. Call ranking function any function acting from the ranking over the family of the subsets of a given finite set N to the ranking on the set N itself. Consider a short list of independent properties such a function should fulfill, and prove that this set of properties characterizes a precise function. We propose and illustrate a list of four properties, and we prove that this list is sufficient to define a unique ranking function. We also prove that the properties are independent, we discuss a dual approach, and we illustrate some possible variants of the problem.

Keywords: Social choice ranking neutrality coalitional anonimity monotonicity

M. A. López Cerdá, G. Beer, M. J. Cánovas Cánovas, J. Parra López

E. Vercher González, J. D. Bermúdez

M. J. Cánovas Cánovas, G. Beer, M. A. López Cerdá, J. Parra López