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Single-switch preferences and the Ostrogorski paradox

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  • Laffond, G.
  • Laine, J.

Abstract

The Ostrogorski paradox refers to the possibility for a democratically chosen program involving finitely many binary decisions to be unpopular. It deals with the potential conflict arising between two majority-based choice procedures from a set of alternatives {− 1, 1}N, where N stands for the number of decisions. The first procedure is the simple majority rule applied decision-wise. In the second procedure, voters valuate programs through their symmetric distance to an ideal, and programs are compared according to the simple majority rule. This paper characterizes the preference domain (i.e., the set of ideals) which allows to avoid the paradox for any number of voters and any number of decisions. We prove that such a domain contains all those preference profiles sharing a property called single-switchness, of which we provide alternative interpretations.
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Suggested Citation

  • Laffond, G. & Laine, J., 2006. "Single-switch preferences and the Ostrogorski paradox," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 49-66, July.
  • Handle: RePEc:eee:matsoc:v:52:y:2006:i:1:p:49-66
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    References listed on IDEAS

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    1. Deb, Rajat & Kelsey, David, 1987. "On constructing a generalized ostrogorski paradox: Necessary and sufficient conditions," Mathematical Social Sciences, Elsevier, vol. 14(2), pages 161-174, October.
    2. Steven J. Brams & William S. Zwicker & D. Marc Kilgour, 1998. "The paradox of multiple elections," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(2), pages 211-236.
    3. List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, vol. 18(01), pages 89-110, April.
    4. Marco Scarsini, 1998. "A strong paradox of multiple elections," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(2), pages 237-238.
    5. Laffond, Gilbert & Laine, Jean, 2000. "Representation in majority tournaments," Mathematical Social Sciences, Elsevier, vol. 39(1), pages 35-53, January.
    6. Christian List, 2005. "The probability of inconsistencies in complex collective decisions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(1), pages 3-32, May.
    7. Hannu Nurmi, 1998. "Voting paradoxes and referenda," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(3), pages 333-350.
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    Citations

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    Cited by:

    1. Nicolas Gabriel Andjiga & Issofa Moyouwou & Monge Kleber Kamdem Ouambo, 2017. "Avoiding Majority Dissatisfaction on a Series of Majority Decisions," Group Decision and Negotiation, Springer, vol. 26(3), pages 453-471, May.
    2. G. Laffond & J. Lainé, 2013. "Unanimity and the Anscombe’s paradox," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 590-611, October.
    3. Nicolas Gabriel Andjiga & Issofa Moyouwou & Monge Kleber Kamdem Ouambo, 0. "Avoiding Majority Dissatisfaction on a Series of Majority Decisions," Group Decision and Negotiation, Springer, vol. 0, pages 1-19.
    4. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, vol. 145(2), pages 512-543, March.
    5. Pablo Amorós & M. Puy, 2010. "Indicators of electoral victory," Public Choice, Springer, vol. 144(1), pages 239-251, July.
    6. repec:spr:grdene:v:21:y:2012:i:4:d:10.1007_s10726-010-9226-2 is not listed on IDEAS
    7. Gilbert Laffond & Jean Lainé, 2014. "Triple-consistent social choice and the majority rule," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 784-799, July.
    8. repec:spr:qualqt:v:51:y:2017:i:4:d:10.1007_s11135-016-0361-y is not listed on IDEAS
    9. Gilbert Laffond & Jean Lainé, 2009. "Condorcet choice and the Ostrogorski paradox," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(2), pages 317-333, February.
    10. Tuğçe Çuhadaroğlu & Jean Lainé, 2012. "Pareto efficiency in multiple referendum," Theory and Decision, Springer, vol. 72(4), pages 525-536, April.
    11. Gilbert Laffond & Jean Lainé, 2008. "The Budget-Voting Paradox," Theory and Decision, Springer, vol. 64(4), pages 447-478, June.

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