Advertisement

Social Choice and Welfare

, Volume 42, Issue 3, pp 735–750 | Cite as

Condorcet winners on median spaces

  • Berno Buechel
Original Paper
  • 233 Downloads

Abstract

We characterize the outcome of majority voting for single-peaked preferences on median spaces. This large class of preferences covers a variety of multi-dimensional policy spaces including products of lines (e.g. grids), trees, and hypercubes. Our main result is the following: If a Condorcet winner (i.e. a winner in pairwise majority voting) exists, then it coincides with the appropriately defined median (“the median voter”). This result generalizes previous findings which are either restricted to a one-dimensional policy space or to the assumption that any two voters with the same preference peak must have identical preferences. The result applies to models of spatial competition between two political candidates. A bridge to the graph-theoretic literature is built.

Keywords

Nash Equilibrium Majority Vote Median Voter Political Competition Condorcet Winner 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

I thank Veronica Block, Dinko Dimitrov, Jan-Philip Gamp, Anke Gerber, Claus-Jochen Haake, Tim Hellmann, Dominik Karos, Gerd Muehlheusser, Clemens Puppe, Nils Roehl, Walter Trockel, and the participants of the “Public Economic Theory (PET 10)” Conference in Istanbul and the “SING 9” Workshop in Budapest for helpful discussions and comments. Moreover, this paper has benefited from the suggestions of two anonymous referees.

References

  1. Ballester M, Haeringer G (2011) A characterization of the single-peaked domain. Soc Choice Welf 36(2):305–322CrossRefGoogle Scholar
  2. Bandelt H-J (1985) Networks with Condorcet solutions. Eur J Oper Res 20(3):314–326CrossRefGoogle Scholar
  3. Bandelt H-J, Barthélémy J-P (1984) Medians in median graphs. Discret Appl Math 8(2):131–142CrossRefGoogle Scholar
  4. Black D (1948) On the rationale of group decision-making. J Polit Econ 56(1):23–34CrossRefGoogle Scholar
  5. Congleton R (2002) The median voter model. In: Rowley F, Schneider RK (eds) The Encyclopedia of public choice. Kluwer Academic Publishers, DordrechtGoogle Scholar
  6. Demange G (1982) Single-peaked orders on a tree. Math Soc Sci 3(4):389–396CrossRefGoogle Scholar
  7. Demange G (2011) Majority relation and median representative ordering. J Span Econ Assoc, 1–15Google Scholar
  8. Downs A (1957) An economic theory of democracy. Harper and Row, New YorkGoogle Scholar
  9. Eaton BC, Lipsey RG (1975) The principle of minimum differentiation reconsidered: some new developments in the theory of spatial competition. Rev Econ Stud 42(1):27–49CrossRefGoogle Scholar
  10. Eiselt HA, Laporte G (1989) Competitive spatial models. Eur J Oper Res, 39–231Google Scholar
  11. Eiselt HA, Laporte G (1993) The existence of equilibria in the 3-facility Hotelling model in a tree. Transp Sci 27(1):39–43CrossRefGoogle Scholar
  12. Hansen P, Thisse JF, Wendell RE (1986) Equivalence of solutions to network location problems. Math Oper Res 11:672–678CrossRefGoogle Scholar
  13. Hotelling H (1929) Stability in competition. Econ J 39(153):41–57CrossRefGoogle Scholar
  14. Moulin H (1980) On strategy-proofness and single peakedness. Public Choice 35(4):437–455CrossRefGoogle Scholar
  15. Moulin H (1984) Generalized Condorcet-winners for single peaked and single-plateau preferences. Soc Choice Welf 1:127–147. doi: 10.1007/BF00452885 CrossRefGoogle Scholar
  16. Nehring K, Puppe C (2007a) Efficient and strategy-proof voting rules: a characterization. Games Econ Behav 59(1):132–153CrossRefGoogle Scholar
  17. Nehring K, Puppe C (2007b) The structure of strategy-proof social choice. Part I: general characterization and possibility results on median spaces. J Econ Theory 135(1):269–305CrossRefGoogle Scholar
  18. Osborne MJ, Slivinski A (1996) A model of political competition with citizen-candidates. Q J Econ 111(1):65–96CrossRefGoogle Scholar
  19. Roemer JE (2001) Political competition: theory and applications. Harvard University Press, CambridgeGoogle Scholar
  20. Van de Vel M (1993) Theory of convex structures. North-HollandGoogle Scholar
  21. Wendell RE, McKelvey RD (1981) New perspectives in competitive location theory. Eur J Oper Res 6(2):174–182CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of HamburgHamburgGermany

Personalised recommendations