Theory and Decision

, Volume 79, Issue 1, pp 1–13 | Cite as

Conditions on social-preference cycles

  • Susumu CatoEmail author


Since Condorcet discovered the voting paradox in the simple majority rule, many scholars have tried to investigate conditions that yield “social-preference cycles”. The paradox can be extended to two main approaches. On the one hand, Kenneth Arrow developed a general framework of social choice theory; on the other hand, direct generalizations of the paradox were offered. The motivation and surface meaning of the two approaches are different, as are the assumed background conditions. In this paper, we investigate the relationship between the two approaches by taking a close look at two works, Ferejohn and Fishburn (J Econ Theory 21:28–45, 1979) and Schwartz (J Econ Theory 137:688–695, 2007).


Voting mechanism Social-preference cycle Voting paradox Decisiveness Generalization 

JEL Classification

D71 D72 



I am grateful to anonymous referees, Tomohiko Kawamori, Toyotaka Sakai, Tomoichi Shinotsuka, and Kotaro Suzumura for helpful comments. This paper was financially supported by Grant-in-Aid for Young Scientists (B) from the Japan Society for the Promotion of Science and the Ministry of Education, Culture, Sports, Science and Technology.


  1. Arrow, K. J. (1951). 1963. Social choice and individual values (2nd ed.). New York: Wiley.Google Scholar
  2. Banks, J. S. (1995). Acyclic social choice from finite sets. Social Choice and Welfare, 12, 293–310.CrossRefGoogle Scholar
  3. Blair, D. H., & Pollak, R. A. (1982). Acyclic collective choice rules. Econometrica, 50, 931–943.CrossRefGoogle Scholar
  4. Bossert, W., & Suzumura, K. (2008). A characterization of consistent collective choice rules. Journal of Economic Theory, 138, 311–320.CrossRefGoogle Scholar
  5. Brams, S. J., & Fishburn, P. C. (2002). Voting procedures. In K. J. Arrow, A. K. Sen, & K. Suzumura (Eds.), Handbook of social choice and welfare (Vol. 1, pp. 173–236). Amsterdam: Elsevier.CrossRefGoogle Scholar
  6. Brown, D. J. (1975). Aggregation of preferences. Quarterly Journal of Economics, 89, 456–469.CrossRefGoogle Scholar
  7. Cato, S., & Hirata, D. (2010). Collective choice rules and collective rationality: A unified method of characterizations. Social Choice and Welfare, 34, 611–630.CrossRefGoogle Scholar
  8. Ferejohn, J. A., & Fishburn, P. C. (1979). Representations of binary decision rules by generalized decisiveness structures. Journal of Economic Theory, 21, 28–45.CrossRefGoogle Scholar
  9. Gehrlein, W. V. (1983). Condorcet’s paradox. Theory and Decision, 15, 161–197.CrossRefGoogle Scholar
  10. Gehrlein, W. V., & Fishburn, P. C. (1976). Condorcet’s paradox and anonymous preference profiles. Public Choice, 26, 1–18.CrossRefGoogle Scholar
  11. Gibbard, A. (2014) Social choice and the Arrow conditions. Economics and Philosophy. doi: 10.1017/S026626711400025X.
  12. Kelsey, D. (1984). Acyclic choice without the Pareto principle. Review of Economic Studies, 51, 693–699.CrossRefGoogle Scholar
  13. Kelsey, D. (1985). Acyclic choice and group veto. Social Choice and Welfare, 2, 131–137.CrossRefGoogle Scholar
  14. Le Breton, M., & Truchon, M. (1995). Acyclicity and the dispersion of the veto power. Social Choice and Welfare, 12, 43–58.CrossRefGoogle Scholar
  15. Mas-Colell, A., & Sonnenschein, H. (1972). General possibility theorems for group decisions. Review of Economic Studies, 39, 185–192.CrossRefGoogle Scholar
  16. Nakamura, K. (1979). The vetoers in a simple game with ordinal preferences. International Journal of Game Theory, 8, 55–61.CrossRefGoogle Scholar
  17. Riker, W. H. (1961). Voting and the summation of preferences: An interpretive bibliographic review of selected developments during the last decade. American Political Science Review, 55, 900–911.CrossRefGoogle Scholar
  18. Sanver, M. R., & Selçuk, Ö. (2010). A characterization of the Copeland solution. Economics Letters, 107, 354–355.CrossRefGoogle Scholar
  19. Schwartz, T. (2007). A procedural condition necessary and sufficient for cyclic social preference. Journal of Economic Theory, 137, 688–695.CrossRefGoogle Scholar
  20. Sen, A. K. (1970). Collective choice and social welfare. San Francisco: Holden-Day.Google Scholar
  21. Sen, A. K. (1979). Personal utilities and public judgements: Or what’s wrong with welfare economics. Economic Journal 89, 537–558.Google Scholar
  22. Suzumura, K. (1976). Remarks on the theory of collective choice. Economica, 43, 381–390.CrossRefGoogle Scholar
  23. Szpilrajn, S. (1930). Sur l’extension de l’ordre partiel. Fundamenta Mathematicae, 16, 386–389.Google Scholar
  24. Truchon, M. (1995). Voting games and acyclic collective choice rules. Mathematical Social Sciences, 29, 165–179.CrossRefGoogle Scholar
  25. Truchon, M. (1996). Acyclicity and decisiveness structures. Journal of Economic Theory, 69, 447–469.CrossRefGoogle Scholar
  26. Tullock, G. (2005). Problems of voting. Public Choice, 123, 49–58.CrossRefGoogle Scholar
  27. Ward, B. (1961). Majority rule and allocation. Journal of Conflict Resolution, 5, 380–389.CrossRefGoogle Scholar
  28. Weber, J. S. (1993). An elementary proof of the conditions for a generalized Condorcet paradox. Public Choice, 77, 415–419.CrossRefGoogle Scholar
  29. Young, H. P. (1974). An axiomatization of Borda’s rule. Journal of Economic Theory, 9, 43–52.CrossRefGoogle Scholar
  30. Young, H. P. (1988). Condorcet’s theory of voting. American Political Science Review, 82, 1231–1244.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institute of Social ScienceThe University of TokyoTokyoJapan

Personalised recommendations