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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Brams, S.J., Kilgour, M.D., Sanver, M.R.: A minimax procedure for negotiating multilateral treaties. In: Wiberg, M. (ed.) Reasoned choices: Essays in Honor of Hannu Nurmi. Finnish Political Science Association, Turku (2004)
Dietrich, F., List, C.: Majority voting on restricted domains. Mimeo (2007)
Dokow, E., Holzman, R.: Aggregation of binary evaluations. Journal of Economic Theory (2008), doi:10.1016/j.jet.2007.10.004
List, C.: The probability of inconsistencies in complex collective decisions. Social Choice and Welfare 24, 3–32 (2005)
List, C., Puppe, C.: Judgment aggregation. In: Anand, P., Pattanaik, P.K., Puppe, C. (eds.) The Handbook of Rational and Social Choice: An Overview of New Foundations and Applications. Oxford University Press, Oxford (2009)
Nurmi, H.: Comparing voting systems. D. Reidel, Dordrecht (1987)
Nurmi, H.: Voting paradoxes and how to deal with them. Springer, Berlin (1999)
Rubinstein, A., Fishburn, P.C.: Algebraic aggregation theory. Journal of Economic Theory 38, 63–77 (1986)
Saari, D.G.: Basic geometry of voting. Springer, Berlin (1995)
Saari, D.G.: Disposing dictators, demystifying voting paradoxes: Social choice analysis. Cambridge University Press, New York (2008)
Wilson, R.: On the theory of aggregation. Journal of Economic Theory 10, 89–99 (1975)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Eckert, D., Klamler, C. (2009). A Geometric Approach to Paradoxes of Majority Voting in Abstract Aggregation Theory. In: Rossi, F., Tsoukias, A. (eds) Algorithmic Decision Theory. ADT 2009. Lecture Notes in Computer Science(), vol 5783. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04428-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-04428-1_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04427-4
Online ISBN: 978-3-642-04428-1
eBook Packages: Computer ScienceComputer Science (R0)