Skip to main content
Log in

Acyclic social choice from finite sets

  • Published:
Social Choice and Welfare Aims and scope Submit manuscript

Abstract

This paper characterizes acyclic preference aggregation rules under various combinations of monotonicity, neutrality, decisiveness, and anonymity, in the spirit of Nakamura's (1979) Theorem on the core of simple games. Each of these characterizations can be seen to follow from Ferejohn and Fishburn's (1979) result on acyclic aggregation rules assuming only independence of irrelevant alternatives. We then state as corollaries to these characterizations extant results such as Sen's (1970) liberal paradox, Blau and Deb's (1977) theorem on the existence of vetoers, and Brown's (1975) theorem on the non-emptiness of the collegium.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Jeffrey Sanford Russell, John Hawthorne & Lara Buchak

References

  • Arrow K (1951) Social Choice and Individual Values. New York: Wiley

    Google Scholar 

  • Blair D, Pollack R (1982) Acyclic collective choice rules. Econometrica 50: 931–93

    Google Scholar 

  • Blau J, Deb R (1977) Social decision functions and the veto. Econometrica 45: 871–879

    Google Scholar 

  • Brown D (1975) Aggregation of preferences. Quarterly J Econ, 89: 456–469

    Google Scholar 

  • Ferejohn J, Fishburn P (1979) Representations of binary decision rules by generalized decisive structures. J Econ Theory 21: 28–45

    Google Scholar 

  • Ferejohn J, Grether D (1974) On a class of rational social decision procedures. J Econ Theory 8: 471–482

    Google Scholar 

  • Le Breton M, Truchon M (1993) Acyclicity and the dispersion of veto power, Cahier 9317, Groupe de Recherche en Politique Economique, Universite Laval

  • Moulin H (1985) From social welfare orderings to acyclic aggregation of preferences. Math Soc Sciences 9: 1–17

    Google Scholar 

  • Moulin H (1988) Axioms of cooperative decision making. Cambridge: Cambridge University Press

    Google Scholar 

  • Nakamura K (1979) The vetoers in a simple game with ordinal preferences. Int J Game Theory 8: 55–61

    Google Scholar 

  • Schofield N (1985) Social choice and democracy. Berlin: Springer

    Google Scholar 

  • Sen A (1970) Collective choice and social welfare. San Francisco: Holden-Day

    Google Scholar 

  • Truchon M (1993) Acyclicity and decisiveness structures, Cahier 9316, Groupe de Recherche en Politique Economique, Universite Laval

  • von Neumann J, Morgenstern O (1974) The theory of games and economic behavior. Princeton: Princeton University Press

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

I thank David Austen-Smith, Michel Le Breton, Maurice Salles, and two anonymous referees for numerous enlightening conversations and comments. I also thank the National Science Foundation and Sloan Foundation for generous financial assistance.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Banks, J.S. Acyclic social choice from finite sets. Soc Choice Welfare 12, 293–310 (1995). https://doi.org/10.1007/BF00179983

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00179983

Keywords

Navigation