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Vetoer and tie-making group theorems for indifference-transitive aggregation rules

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  • Jun Iritani
  • Tomoyuki Kamo
  • Ryo-ichi Nagahisa

Abstract

A binary relation is indifference-transitive if its symmetric part satisfies the transitivity axiom. We investigated the properties of Arrovian aggregation rules that generate acyclic and indifference-transitive social preferences. We proved that there exists unique vetoer in the rule if the number of alternatives is greater than or equal to four. We provided a classification of decisive structures in aggregation rules where the number of alternatives is equal to three. Furthermore, we showed that the coexistence of a vetoer and a tie-making group, which generates social indifference, is inevitable if the rule satisfies the indifference unanimity. The relationship between the vetoer and the tie-making group, i.e., whether the vetoer belongs to the tie-making group or not, determines the power structure of the rule. Copyright Springer-Verlag 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sochwe:v:40:y:2013:i:1:p:155-171
    DOI: 10.1007/s00355-011-0591-9
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    References listed on IDEAS

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    1. Ferejohn, John A. & Fishburn, Peter C., 1979. "Representations of binary decision rules by generalized decisiveness structures," Journal of Economic Theory, Elsevier, vol. 21(1), pages 28-45, August.
    2. Blair, Douglas H & Pollak, Robert A, 1982. "Acyclic Collective Choice Rules," Econometrica, Econometric Society, vol. 50(4), pages 931-943, July.
    3. Donald J. Brown, 1975. "Aggregation of Preferences," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 89(3), pages 456-469.
    4. Le Breton, M. & Truchon, M., 1993. "Acyclicity and the Dispersion of the Veto Power," Papers 9317, Laval - Recherche en Politique Economique.
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    Cited by:

    1. Susumu Cato, 2018. "Infinite Population and Positive Responsiveness: A Note," Economics Bulletin, AccessEcon, vol. 38(1), pages 196-200.
    2. Cato, Susumu, 2015. "Weak independent decisiveness and the existence of a unique vetoer," Economics Letters, Elsevier, vol. 131(C), pages 59-61.
    3. Kamo, Tomoyuki & Nagahisa, Ryo-Ichi, 2016. "Arrovian social choice with psychological thresholds," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 93-99.
    4. Cato, Susumu, 2017. "Unanimity, anonymity, and infinite population," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 28-35.
    5. Susumu Cato, 2019. "The possibility of Paretian anonymous decision-making with an infinite population," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(4), pages 587-601, December.

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