The Libertarian Identification Rule in Finite Atomistic Lattices

Collective Identification Procedures (CIPs) model admission rules regulating membership in associations, communities and clubs: the Libertarian identification rule Fl is the CIP which essentially relies on self-certification. This paper studies Fl in an arbitrary finite atomistic lattice, allowing an unified treatment of collective identification problems with either exogenous or endogenous choice of classification labels. An elementary axiomatic characterization of Fl in that general setting is provided and contrasted with previously known characterizations which only work in more specialized (e.g. distributive) lattices, and are therefore confined to collective identification problems with exogenously fixed labels. Non-manipulability properties of Fl on a certain simple restricted domain are also considered and shown to hold for any finite atomistic lattice