A geometric approach to paradoxes of majority voting in abstract aggregation theory

Abstract

In this paper we extend Saari's geometric approach to paradoxes of preference aggregation to the analysis of paradoxes of majority voting in a more general setting like Anscombe's paradox and paradoxes of judgment aggregation. In particular we use Saari's representation cubes to provide a geometric representation of profiles and majority outcomes. Within this geometric framework, we show how profile decompositions can be used to derive restrictions on profiles that avoid the paradoxes of majority voting. © 2009 Springer-Verlag Berlin Heidelberg.