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Aggregation of binary evaluations: a Borda-like approach

Author

Listed:
  • Conal Duddy

    () (National University of Ireland Galway)

  • Ashley Piggins

    () (National University of Ireland Galway)

  • William S. Zwicker

    () (Union College)

Abstract

Abstract We characterize a rule for aggregating binary evaluations—equivalently, dichotomous weak orders—similar in spirit to the Borda rule from the preference aggregation literature. The binary evaluation framework was introduced as a general approach to aggregation by Wilson (J Econ Theory 10:89–99, 1975). In this setting we characterize the “mean rule,” which we derive from properties similar to those Young (J Econ Theory 9:43–52, 1974) used in his characterization of the Borda rule. Complementing our axiomatic approach is a derivation of the mean rule using vector decomposition methods that have their origins in Zwicker (Math Soc Sci 22:187–227, 1991). Additional normative appeal is provided by a form of tension minimization that characterizes the mean rule and suggests contexts wherein its application may be appropriate. Finally, we derive the mean rule from an approach to judgment aggregation recently proposed by Dietrich (Soc Choice Welf 42:873–911, 2014).

Suggested Citation

  • Conal Duddy & Ashley Piggins & William S. Zwicker, 2016. "Aggregation of binary evaluations: a Borda-like approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(2), pages 301-333, February.
  • Handle: RePEc:spr:sochwe:v:46:y:2016:i:2:d:10.1007_s00355-015-0914-3
    DOI: 10.1007/s00355-015-0914-3
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    References listed on IDEAS

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    1. 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.
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    Citations

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    Cited by:

    1. Dietrich, Franz, 2015. "Aggregation theory and the relevance of some issues to others," Journal of Economic Theory, Elsevier, vol. 160(C), pages 463-493.
    2. Dietrich, Franz, 2016. "Judgment aggregation and agenda manipulation," Games and Economic Behavior, Elsevier, vol. 95(C), pages 113-136.
    3. Jérôme Lang & Gabriella Pigozzi & Marija Slavkovik & Leendert Torre & Srdjan Vesic, 2017. "A partial taxonomy of judgment aggregation rules and their properties," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 327-356, February.
    4. Dietrich, Franz, 2015. "Aggregation theory and the relevance of some issues to others," Journal of Economic Theory, Elsevier, vol. 160(C), pages 463-493.

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    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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