Theory and Decision

, Volume 75, Issue 4, pp 563–579 | Cite as

Social choice, the strong Pareto principle, and conditional decisiveness

  • Susumu CatoEmail author


This paper examines social choice theory with the strong Pareto principle. The notion of conditional decisiveness is introduced to clarify the underlying power structure behind strongly Paretian aggregation rules satisfying binary independence. We discuss the various degrees of social rationality: transitivity, semi-transitivity, the interval-order property, quasi-transitivity, and acyclicity.


Arrow’s impossibility theorem Strong Pareto  Ultrafilter Conditional decisiveness Serial dictatorship 

JEL Classification




I thank Tomoki Inoue and an anonymous referee of this journal for constructive suggestions. 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. Aliprantis, C. D., & Border, K. C. (2006). Infinite dimensional analysis: A hitchhiker’s guide. Berlin: Springer Verlag.Google Scholar
  2. Arrow, K. J. (1951). Social choice and individual values (2nd ed., 1963). New York: Wiley.Google Scholar
  3. Banks, J. S. (1995). Acyclic social choice from finite sets. Social Choice and Welfare, 12, 293–310.CrossRefGoogle Scholar
  4. Blair, D. H., Bordes, G., Kelly, J. S., & Suzumura, K. (1975). Impossibility theorems without collective rationality. Journal of Economic Theory, 13, 361–379.CrossRefGoogle Scholar
  5. Blair, D. H., & Pollak, R. A. (1979). Collective rationality and dictatorship: The scope of the Arrow theorem. Journal of Economic Theory, 21, 186–194.CrossRefGoogle Scholar
  6. Blau, J. H. (1979). Semiorders and collective choice. Journal of Economic Theory, 21, 195–206.CrossRefGoogle Scholar
  7. Bossert, W., & Suzumura, K. (2008). A characterization of consistent collective choice rules. Journal of Economic Theory, 138, 311–320.CrossRefGoogle Scholar
  8. Bossert, W., & Suzumura, K. (2009). Decisive coalitions and coherence properties. CIREQ: Discussion Paper, Université de Montréal.Google Scholar
  9. Bossert, W., & Suzumura, K. (2010). Consistency, choice and rationality. Cambridge: Harvard University Press.Google Scholar
  10. Bossert, W., & Suzumura, K. (2011). Multi-profile intergenerational social choice. Social Choice and Welfare, 37, 493–509.CrossRefGoogle Scholar
  11. Brown, D. J. (1974). An approximate solution to Arrow’s problem. Journal of Economic Theory, 9, 375–383.CrossRefGoogle Scholar
  12. Brown, D. J. (1975). Aggregation of preferences. Quarterly Journal of Economics, 89, 456–469.CrossRefGoogle Scholar
  13. Campbell, K., & Kelly, J. S. (2002). Impossibility theorems in the Arrovian framework. In K. J. Arrow, A. K. Sen, & K. Suzumura (Eds.), Handbook of social choice and welfare (Vol. 1, pp. 35–94). North-Holland: Amsterdam.CrossRefGoogle Scholar
  14. Cato, S. (2011). Pareto principles, positive responsiveness, and majority decisions. Theory and Decision, 71, 503–518.CrossRefGoogle Scholar
  15. Cato, S. (2012a). Quasi-decisiveness, quasi-ultrafilter, and social quasi-orderings. Social Choice and Welfare. doi: 10.1007/s00355-012-0677-z.
  16. Cato, S. (2012b). Social choice without the Pareto principle: A comprehensive analysis. Social Choice and Welfare, 39, 869–889.CrossRefGoogle Scholar
  17. Cato, S. (2013). Remarks on Suzumura consistent collective choice rules. Mathematical Social Sciences, 65, 40–47.CrossRefGoogle Scholar
  18. 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
  19. Ferejohn, J., & Page, T. (1978). On the foundations of intertemporal choice. American Journal of Agricultural Economics, 60, 269–275.CrossRefGoogle Scholar
  20. Fishburn, P. C. (1970). Arrow’s impossibility theorem: Concise proof and infinite voters. Journal of Economic Theory, 2, 103–106.CrossRefGoogle Scholar
  21. Fishburn, P. C. (1975). Axioms for lexicographic preferences. Review of Economic Studies, 42, 415–419.CrossRefGoogle Scholar
  22. Gibbard, A. (1969). Social choice and the Arrow condition. Unpublished paper.Google Scholar
  23. Guha, A. (1972). Neutrality, monotonicity, and the right of veto. Econometrica, 40, 821–826.CrossRefGoogle Scholar
  24. Hansson, B. (1976). The existence of group preference functions. Public Choice, 28, 89–98.CrossRefGoogle Scholar
  25. Kirman, A. P., & Sondermann, D. (1972). Arrow’s theorem, many agents, and invisible dictators. Journal of Economic Theory, 5, 267–277.CrossRefGoogle Scholar
  26. Mas-Colell, A., & Sonnenschein, H. (1972). General possibility theorems for group decisions. Review of Economic Studies, 39, 185–192.CrossRefGoogle Scholar
  27. Packel, E. W. (1980). Impossibility results in the axiomatic theory of intertemporal choice. Public Choice, 35, 219–227.CrossRefGoogle Scholar
  28. Packel, E. W. (1981). Social decision functions and strongly decisive sets. Review of Economic Studies, 48, 343–349.CrossRefGoogle Scholar
  29. Sen, A. K. (1969). Quasi-transitivity, rational choice and collective decisions. Review of Economic Studies, 36, 381–393.CrossRefGoogle Scholar
  30. Sen, A. K. (1970). Collective choice and social welfare. San Francisco: Holden-Day.Google Scholar
  31. Suzumura, K. (1976). Remarks on the theory of collective choice. Economica, 43, 381–390.CrossRefGoogle Scholar
  32. Willard, S. (1970). General topology. Reading: Addison-Wesley Publishing Company.Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Graduate School of Social SciencesTokyo Metropolitan UniversityHachioji-shiJapan

Personalised recommendations