Daniela Bubboloni, Università di Firenze

Permutation groups and democracy

Abstract: In this seminar we explore how actions of permutation groups can be used to deal with problems in social choice theory, the mathematical description of democracy. The main ideas of social choice theory are introduced  by the use of symmetric groups, letting the tension among resoluteness, anonymity and neutrality for social choice correspondences emerge. Generalizing a famous theorem by H. Moulin, we introduce a concept of regularity for a special class of permutation groups,  which is rich in applications in social choice theory but also interesting from a pure group theoretical point of view.