www.accedoverlag.d e A Geometric Approach to Paradoxes of Majority Voting: From Anscombe’s Paradox to the Discursive

Abstract Among many other topics, Hannu Nurmi has worked on voting para-doxes and how to deal with them. In his work he often uses a geometric approach developed by Don Saari for the analysis of paradoxes of preference aggregation such as the Condorcet paradox or Arrow’s general possibility theorem. In this paper we extend his approach to other paradoxes analysed by Nurmi and the recent work in 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. Moreover, we use our frame-work to determine the likelihood of those paradoxes. Finally, current distance-based approaches in judgment aggregation are discussed within our framework