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The B.E. Journal of Theoretical Economics

Editor-in-Chief: Schipper, Burkhard

Ed. by Fong, Yuk-fai / Peeters, Ronald / Puzzello , Daniela / Rivas, Javier / Wenzelburger, Jan

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Hybrid Invariance and Oligarchic Structures

Susumu Cato
  • Corresponding author
  • Postdoctoral Fellow for Research Abroad of the Japan Society for the Promotion of Science, Institute of Social Science, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
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Published Online: 2017-11-16 | DOI: https://doi.org/10.1515/bejte-2016-0145


This study addresses the problem of Arrovian preference aggregation. Social rationality plays a crucial role in the standard Arrovian framework. However, no assumptions on social rationality are imposed here. Social preferences are allowed to be any binary relation (possibly incomplete and intransitive). We introduce the axiom of hybrid invariance, which requires that if social preferences under two preference profiles make the same judgment, then a social preference under a “hybrid” of the two profiles must extend the original judgment in a certain way. Then, we characterize the structure of decisive coalitions under hybrid invariance.

Keywords: social choice; Arrow’s impossibility theorem; filter, hybrid invariance; Oligarchy

JEL Classification: D71


  • Arrow, K. J. 1963. Social Choice and Individual Values, 2nd ed. New York: Wiley.Google Scholar

  • Banks, J. S. 1995. “Acyclic Social Choice From Finite Sets.” Social Choice and Welfare 12 (3):293-310.Google Scholar

  • Bossert, W., and Suzumura K. 2011. “Multi-profile Intergenerational Social Choice.” Social Choice and Welfare 37 (3):493–509.Web of ScienceCrossrefGoogle Scholar

  • Brown, D. J. 1974. “An Approximate Solution to Arrow’s Problem.” Journal of Economic Theory 9 (4):375-383.CrossrefGoogle Scholar

  • Brown, D. J. 1975. “Aggregation of Preferences.” Quarterly Journal of Economics 89 (3):456–469.CrossrefGoogle Scholar

  • Buchanan, J. M. 1954. “Social Choice, Democracy, and free Markets.” Journal of Political Economy 62 (2):114–123.CrossrefGoogle Scholar

  • Cato, S. 2012. “Social Choice Without the Pareto Principle: A Comprehensive Analysis.” Social Choice and Welfare 39 (4):869–889.Web of ScienceCrossrefGoogle Scholar

  • Cato, S. 2013a. “Social Choice, the Strong Pareto Principle, and Conditional Decisiveness.” Theory and Decision 75 (4):563–579.CrossrefWeb of ScienceGoogle Scholar

  • Cato, S. 2013b. “Quasi-Decisiveness, Quasi-Ultrafilter, and Social Quasi-Orderings.” Social Choice and Welfare 41 (1):169–202.Web of ScienceCrossrefGoogle Scholar

  • Cato, S. 2016. Rationality and Operators: The Formal Structure of Preferences. Singapore: Springer.Google Scholar

  • Denicolò, V. 1993. “Fixed Agenda Social Choice Theory: Correspondence and Impossibility Theorems for Social Choice Correspondences and Social Decision Functions.” Journal of Economic Theory 59 (2):324–332.CrossrefGoogle Scholar

  • Denicolò, V. 1998. “Independent Decisiveness and the Arrow Theorem.” Social Choice and Welfare 15 (4):563–566.CrossrefGoogle Scholar

  • Fey, M. 2004. “May’s Theorem with an Infinite Population.” Social Choice and Welfare 23 (2):275-293.Google Scholar

  • Fishburn, P. C. 1970. “Arrow’s Impossibility Theorem: Concise Proof and Infinite Voters.” Journal of Economic Theory 2 (1):103–106.CrossrefGoogle Scholar

  • Fishburn, P. C. 1987. Interprofile Conditions and Impossibility. Newark: Harwood Academic Publishers GmbH.Google Scholar

  • Gibbard, A. 2014. “Social Choice and the Arrow Conditions.” Economics and Philosophy 30 (3): 269–284. DOI: . .CrossrefWeb of ScienceGoogle Scholar

  • Guha A. 1972. “Neutrality, Monotonicity, and the Right of Veto.” Econometrica 40 (5):821–826.CrossrefGoogle Scholar

  • Hansson, B. 1976. “The Existence of Group Preference Functions.” Public Choice 28 (1):89–98.CrossrefGoogle Scholar

  • Iritani, J., Kamo T., and Nagahisa R. I. 2013. “Vetoer and Tie-Making Group Theorems for Indifference-Transitive Aggregation Rules.” Social Choice and Welfare 40 (1):155–171.CrossrefWeb of ScienceGoogle Scholar

  • Kirman, A. P. and Sondermann D. 1972. “Arrow’s Theorem, Many Agents, and Invisible Dictators.” Journal of Economic Theory 5 (2):267–277.CrossrefGoogle Scholar

  • Mihara, H. R. 1997. “Anonymity and Neutrality in Arrow’s Theorem with Restricted Coalition Algebras.” Social Choice and Welfare 14 (4):503–512.CrossrefGoogle Scholar

  • Noguchi, M. 2011. “Generic Impossibility of Arrow’s Impossibility Theorem.” Journal of Mathematical Economics 47 (4):391–400.CrossrefWeb of ScienceGoogle Scholar

  • Plott, C. R. 1973. “Path Independence, Rationality, and Social Choice.” Econometrica 41 (6):1075–1091.CrossrefGoogle Scholar

  • Sen, A. K. 1993. “Internal Consistency of Choice.” Econometrica 61 (3):495–521.CrossrefGoogle Scholar

  • Shapiro, I. 2009. The State of Democratic Theory. Princeton University Press.Google Scholar

  • Willard, S. 1970. General Topology. Reading, Massachusetts: Addison-Wesley Publishing Company.Google Scholar

About the article

Susumu Cato

Postdoctoral Fellow for Research Abroad of the Japan Society for the Promotion of Science

Published Online: 2017-11-16

Citation Information: The B.E. Journal of Theoretical Economics, Volume 18, Issue 1, 20160145, ISSN (Online) 1935-1704, DOI: https://doi.org/10.1515/bejte-2016-0145.

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