In this paper we describe some research directions in social choice and aggregation theory led at the “Centre de Mathématique Sociale“ since the fifties. We begin by presenting some institutional aspects concerning this EHESS center. Then we sketch a thematic history by considering the...

In a paper published in 1952, shortly after publication of Arrow's celebrated impossibility result, the French mathematicien Georges-Théodule Guilbaud has obtained a dictatorship result for the logical problem of aggregation, thus anticipating the literature on abstract aggregation theory and...

We first present the concept of duality appearing in order theory, i.e. the notions of dual isomorphism and of Galois connection. Then, we describe two fundamental dualities, the duality extension/intention associated with a binary relation between two sets, and the duality between implicational...

In a paper published in 1952, the French mathematician Georges-Théodule Guilbaud has generalized Arrow's impossibility result to the "logical problem of aggregation", thus anticipating the literature on abstract aggregation theory and judgment aggregation. We reconstruct the proof of Guilbaud's...

In this paper, we give a characterization of meet-projections in simple atomistic lattices that generalizes results on the aggregation of partitions in cluster analysis.

Among the many significant contributions of Fishburn to social choice theory some have borne on what he has called «acyclic sets», i.e. these sets of linear orders where majority rule applies without «Condorcet effect» (majority relation never has cycles). Search for large such domains is a...

Condorcet domains are sets of linear orders where Condorcet's effect can never occur. Works of Abello, Chameni-Nembua, Fishburn and Galambos and Reiner have allowed a strong understanding of a significant class of Condorcet domains which are distributive lattices -in fact covering distributive...

In this paper we first study the changes occuring in the posets of irreducible elements when one goes from an arbitrary Moore family (respectively, a convex geometry) to one of its lower covers in the lattice of all Moore families (respectively, in the semilattice of all convex geometries)...

Among the many significant contributions that Fishburn made to social choice theory some have focused on what he has called "acyclic sets", i.e. the sets of linear orders where majority rule applies without the "Condorcet effect" (majority relation never has cycles). The search for large domains...

. In this paper we consider the three classes of choice functionssatisfying the three significant axioms called heredity (H), concordance (C) and outcast (O). We show that the set of choice functions satisfying any one of these axioms is a lattice, and we study the properties of these lattices....