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Measuring consensus in a preference-approval context

Author

Listed:
  • Bora Erdamar

    (X-DEP-ECO - Département d'Économie de l'École Polytechnique - X - École polytechnique, Istanbul Bilgi University)

  • José Luis Garcia-Lapresta

    (PRESAD Research Group - UVa - Universidad de Valladolid [Valladolid])

  • David Pérez-Roman

    (PRESAD Research Group - UVa - Universidad de Valladolid [Valladolid])

  • Remzi Sanver

    (Department of Economics, Bilgi University - Istanbul Bilgi University)

Abstract

We consider measuring the degree of homogeneity for preference-approval profiles which include the approval information for the alternatives as well as the rankings of them. A distance-based approach is followed to measure the disagreement for any given two preference-approvals. Under the condition that a proper metric is used, we propose a measure of consensus which is robust to some extensions of the ordinal framework. This paper also shows that there exists a limit for increasing the homogeneity level in a group of individuals by simply replicating their preference-approvals.

Suggested Citation

  • Bora Erdamar & José Luis Garcia-Lapresta & David Pérez-Roman & Remzi Sanver, 2012. "Measuring consensus in a preference-approval context," Working Papers hal-00681297, HAL.
    • Handle: RePEc:hal:wpaper:hal-00681297
    Note: View the original document on HAL open archive server: https://hal.science/hal-00681297
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    References listed on IDEAS

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    1. Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), 2009. "The Mathematics of Preference, Choice and Order," Studies in Choice and Welfare, Springer, number 978-3-540-79128-7, December.
    2. Steven J. Brams & M. Remzi Sanver, 2009. "Voting Systems that Combine Approval and Preference," Studies in Choice and Welfare, in: Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), The Mathematics of Preference, Choice and Order, pages 215-237, Springer.
    3. Michel Balinski & Rida Laraki, 2011. "Majority Judgment: Measuring, Ranking, and Electing," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262015137, December.
    4. Brams, Steven J. & Fishburn, Peter C., 1978. "Approval Voting," American Political Science Review, Cambridge University Press, vol. 72(3), pages 831-847, September.
    5. Cook, Wade D. & Kress, Moshe & Seiford, Lawrence M., 1997. "A general framework for distance-based consensus in ordinal ranking models," European Journal of Operational Research, Elsevier, vol. 96(2), pages 392-397, January.
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    Cited by:

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    More about this item

    Keywords

    Consensus; Approval voting; Preference-approval; Kemeny metric; Hamming metric;
    All these keywords.

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