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Arrow's theorem with social quasi-orderings

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  • WEYMARK, John

Abstract

The collective rationality requirement in Arrow's theorem is weakened to demanding a social quasi-ordering (a reflexive and transitive but not necessarily complete binary relation). This weakening leads to the existence of a group such that (a) whenever all members of the group strictly prefer one alternative to another then so does society and (b) whenever two members of the group have opposite strict preferences over a pair of alternatives then the pair is socially not ranked. This theorem is then used to provide an axiomatization of the strong Pareto rule. These results are compared and contrasted to Gibbard's oligarchy theorem and Sen's axiomatization of the Pareto extension rule. Copyright Martinus Nijhoff Publishers 1984
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  • WEYMARK, John, 1984. "Arrow's theorem with social quasi-orderings," LIDAM Reprints CORE 609, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:609
    DOI: 10.1007/BF00124943
    Note: In : Public Choice, 42, 235-246, 1984
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    References listed on IDEAS

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    1. Fishburn, Peter C, 1974. "Impossibility Theorems without the Social Completeness Axiom," Econometrica, Econometric Society, vol. 42(4), pages 695-704, July.
    2. Sen, Amartya, 1970. "Interpersonal Aggregation and Partial Comparability," Econometrica, Econometric Society, vol. 38(3), pages 393-409, May.
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    6. Blackorby, Charles & Donaldson, David, 1977. "Utility vs equity : Some plausible quasi-orderings," Journal of Public Economics, Elsevier, vol. 7(3), pages 365-381, June.
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    8. Blackorby, Charles, 1975. "Degrees of Cardinality and Aggregate Partial Orderings," Econometrica, Econometric Society, vol. 43(5-6), pages 845-852, Sept.-Nov.
    9. Blair, Douglas H & Pollak, Robert A, 1982. "Acyclic Collective Choice Rules," Econometrica, Econometric Society, vol. 50(4), pages 931-943, July.
    10. Bengt Hansson, 1976. "The existence of group preference functions," Public Choice, Springer, vol. 28(1), pages 89-98, December.
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    Cited by:

    1. Bossert, Walter & Suzumura, Kotaro, 2012. "Product filters, acyclicity and Suzumura consistency," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 258-262.
    2. Bossert, Walter & Suzumura, Kotaro, 2008. "A characterization of consistent collective choice rules," Journal of Economic Theory, Elsevier, vol. 138(1), pages 311-320, January.
    3. Eisermann, Michael, 2006. "Arrovian juntas," MPRA Paper 81, University Library of Munich, Germany, revised 03 Oct 2006.
    4. Pycia, Marek & Ãœnver, M. Utku, 2020. "Arrovian Efficiency and Auditability in the Allocation of Discrete Resources," CEPR Discussion Papers 15377, C.E.P.R. Discussion Papers.
    5. C. Binder, 2014. "Plural identities and preference formation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 959-976, April.
    6. Matthias Hild, 2004. "A Note On Impossibility Theorems and Seniority Rules," Theory and Decision, Springer, vol. 57(1), pages 69-78, August.
    7. Cato, Susumu, 2018. "Incomplete decision-making and Arrow’s impossibility theorem," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 58-64.
    8. Wesley H. Holliday & Eric Pacuit, 2020. "Arrow’s decisive coalitions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 463-505, March.
    9. Kamaga, Kohei, 2018. "When do utilitarianism and egalitarianism agree on evaluation? An intersection approach," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 41-48.
    10. Marek Pycia & M. Utku Ünver, 2016. "Arrovian Efficiency in Allocation of Discrete Resources," Boston College Working Papers in Economics 916, Boston College Department of Economics.
    11. Adachi, Tsuyoshi & Cato, Susumu & Kamaga, Kohei, 2014. "Extended anonymity and Paretian relations on infinite utility streams," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 24-32.
    12. Piggins, Ashley & Duddy, Conal, 2016. "Oligarchy and soft incompleteness," MPRA Paper 72392, University Library of Munich, Germany.
    13. Conal Duddy & Ashley Piggins, 2018. "On some oligarchy results when social preference is fuzzy," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(4), pages 717-735, December.
    14. Subochev, Andrey & Aleskerov, Fuad & Pislyakov, Vladimir, 2018. "Ranking journals using social choice theory methods: A novel approach in bibliometrics," Journal of Informetrics, Elsevier, vol. 12(2), pages 416-429.
    15. Tsoukias, Alexis, 2008. "From decision theory to decision aiding methodology," European Journal of Operational Research, Elsevier, vol. 187(1), pages 138-161, May.
    16. John A Weymark, 2012. "Social Welfare Functions," Vanderbilt University Department of Economics Working Papers vuecon-sub-13-00018, Vanderbilt University Department of Economics.
    17. Dan Qin, 2014. "Aggregating quasi-transitive preferences: a note," Economics Bulletin, AccessEcon, vol. 34(2), pages 976-983.

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