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Independent, neutral, and monotonic collective choice: the role of Suzumura consistency

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  • Walter Bossert

    (University of Montreal)

  • Susumu Cato

    (University of Tokyo)

  • Kohei Kamaga

    (Sophia University)

Abstract

We examine the impact of Suzumura’s (Economica 43:381–390, 1976) consistency property when applied in the context of collective choice rules that are independent of irrelevant alternatives, neutral, and monotonic. An earlier contribution by Blau and Deb (Econometrica 45:871–879, 1977) establishes the existence of a vetoer if the collective relation is required to be complete and acyclical. The purpose of this paper is to explore the possibilities that result if completeness and acyclicity are dropped and Suzumura consistency is imposed instead. A conceptually similar but logically independent version of the combined axiom that requires the collective decision mechanism to be independent, neutral, and monotonic is employed. In the case of a finite population, we obtain an alternative impossibility theorem if a collective choice rule is assumed to be non-degenerate and a modified no veto requirement is imposed instead of Blau and Deb’s (1977) condition. If the population is countably infinite, the impossibility can be avoided but it resurfaces if our new no veto property is extended to a coalitional variant.

Suggested Citation

  • Walter Bossert & Susumu Cato & Kohei Kamaga, 2023. "Independent, neutral, and monotonic collective choice: the role of Suzumura consistency," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(4), pages 835-852, November.
    • Handle: RePEc:spr:sochwe:v:61:y:2023:i:4:d:10.1007_s00355-023-01472-4
    DOI: 10.1007/s00355-023-01472-4
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    References listed on IDEAS

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    1. Walter Bossert & Kotaro Suzumura, 2015. "Expected utility without full transitivity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 707-722, December.
    2. Kotaro Suzumura, 1978. "On the Consistency of Libertarian Claims," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 45(2), pages 329-342.
    3. Bossert, Walter & Suzumura, Kotaro, 2008. "A characterization of consistent collective choice rules," Journal of Economic Theory, Elsevier, vol. 138(1), pages 311-320, January.
    4. Suzumura, Kotaro, 1999. "Paretian Welfare Judgements and Bergsonian Social Choice," Economic Journal, Royal Economic Society, vol. 109(455), pages 204-220, April.
    5. Donald J. Brown, 1975. "Aggregation of Preferences," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 89(3), pages 456-469.
    6. repec:bla:econom:v:72:y:2005:i:286:p:185-200 is not listed on IDEAS
    7. Cato, Susumu, 2017. "Unanimity, anonymity, and infinite population," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 28-35.
    8. Bossert, Walter & Cato, Susumu, 2021. "Superset-robust collective choice rules," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 126-136.
    9. Bossert, Walter & Cato, Susumu, 2020. "Acyclicity, anonymity, and prefilters," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 134-141.
    10. Susumu Cato, 2013. "Quasi-decisiveness, quasi-ultrafilter, and social quasi-orderings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 169-202, June.
    11. Amartya Sen, 1969. "Quasi-Transitivity, Rational Choice and Collective Decisions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 381-393.
    12. Kotaro Suzumura, 2000. "Presidential Address: Welfare Economics Beyond Welfarist-Consequentialism," The Japanese Economic Review, Japanese Economic Association, vol. 51(1), pages 1-32, March.
    13. Blau, Julian H & Deb, Rajat, 1977. "Social Decision Functions and the Veto," Econometrica, Econometric Society, vol. 45(4), pages 871-879, May.
    14. Bengt Hansson, 1976. "The existence of group preference functions," Public Choice, Springer, vol. 28(1), pages 89-98, December.
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