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Arrovian social choice with psychological thresholds


  • Kamo, Tomoyuki
  • Nagahisa, Ryo-Ichi


This paper studies Arrovian preference aggregation rules–the rules satisfying weak Pareto and Arrow’s independence of irrelevant alternatives (IIA)–when individual preferences are nontransitive due to the existence of psychological thresholds — a problem of perceptible difference. A new domain replaces the universal domain, and rationality requirements of social preferences, i.e., transitivity, quasi-transitivity, and acyclicity with indifference transitivity, are converted into the corresponding versions respectively. We show that the Arrovian impossibilities, i.e., dictator, oligarchy, and vetoer theorems, still survive in this setting.

Suggested Citation

  • Kamo, Tomoyuki & Nagahisa, Ryo-Ichi, 2016. "Arrovian social choice with psychological thresholds," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 93-99.
  • Handle: RePEc:eee:mateco:v:63:y:2016:i:c:p:93-99
    DOI: 10.1016/j.jmateco.2016.01.001

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    References listed on IDEAS

    1. Blau, Julian H., 1979. "Semiorders and collective choice," Journal of Economic Theory, Elsevier, vol. 21(1), pages 195-206, August.
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    3. Fishburn, Peter C, 1970. "Intransitive Individual Indifference and Transitive Majorities," Econometrica, Econometric Society, vol. 38(3), pages 482-489, May.
    4. W. E. Armstrong, 1951. "Utility And The Theory Of Welfare," Oxford Economic Papers, Oxford University Press, vol. 3(3), pages 259-271.
    5. Blair, Douglas H. & Pollak, Robert A., 1979. "Collective rationality and dictatorship: The scope of the arrow theorem," Journal of Economic Theory, Elsevier, vol. 21(1), pages 186-194, August.
    6. Barthelemy, Jean-Pierre, 1982. "Arrow's theorem: unusual domains and extended codomains," Mathematical Social Sciences, Elsevier, vol. 3(1), pages 79-89, July.
    7. Ehud Kalai & Eitan Muller & Mark Satterthwaite, 1979. "Social welfare functions when preferences are convex, strictly monotonic, and continuous," Public Choice, Springer, vol. 34(1), pages 87-97, March.
    8. Jun Iritani & Tomoyuki Kamo & Ryo-ichi Nagahisa, 2013. "Vetoer and tie-making group theorems for indifference-transitive aggregation rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 155-171, January.
    9. Campbell, Donald E. & Kelly, Jerry S., 2002. "Impossibility theorems in the arrovian framework," Handbook of Social Choice and Welfare,in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 1, pages 35-94 Elsevier.
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