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Aggregation of binary evaluations: a Borda-like approach

Author

Listed:
  • Duddy, Conal
  • Piggins, Ashley
  • Zwicker, William

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 (1975) 63-77). In this setting we characterize the "mean rule," which we derive from properties similar to those Young (J. Econ. Theory 9 (1974) 43-52) 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 (1991) 187-227). Finally, we derive the mean rule from an approach to judgment aggregation recently proposed by Dietrich (Soc. Choice. Welf. 42 (2014) 873-911)

Suggested Citation

  • Duddy, Conal & Piggins, Ashley & Zwicker, William, 2014. "Aggregation of binary evaluations: a Borda-like approach," MPRA Paper 62071, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:62071
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    References listed on IDEAS

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    1. Shmuel Nitzan & Ariel Rubinstein, 1981. "A further characterization of Borda ranking method," Public Choice, Springer, vol. 36(1), pages 153-158, January.
    2. List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, vol. 18(1), pages 89-110, April.
    3. Franz Dietrich, 2014. "Scoring rules for judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 873-911, April.
    4. 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.
    5. François Maniquet & Philippe Mongin, 2015. "Approval voting and Arrow’s impossibility theorem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(3), pages 519-532, March.
    6. Franz Dietrich & Christian List, 2007. "Arrow’s theorem in judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(1), pages 19-33, July.
    7. List, Christian & Polak, Ben, 2010. "Introduction to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 441-466, March.
    8. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521808163, September.
    9. Duddy, Conal & Piggins, Ashley, 2013. "Collective approval," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 190-194.
    10. Zwicker, William S., 1991. "The voters' paradox, spin, and the Borda count," Mathematical Social Sciences, Elsevier, vol. 22(3), pages 187-227, December.
    11. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521731607, September.
    12. Bogomolnaia, Anna & Moulin, Herve & Stong, Richard, 2005. "Collective choice under dichotomous preferences," Journal of Economic Theory, Elsevier, vol. 122(2), pages 165-184, June.
    13. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
    14. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521004046, September.
    15. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
    16. repec:hal:pseose:halshs-00978027 is not listed on IDEAS
    17. Young, H. P., 1974. "An axiomatization of Borda's rule," Journal of Economic Theory, Elsevier, vol. 9(1), pages 43-52, September.
    18. Nehring, Klaus & Puppe, Clemens, 2010. "Abstract Arrowian aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 467-494, March.
    19. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521516051, September.
    20. Hans Peters & Souvik Roy & Ton Storcken, 2012. "On the manipulability of approval voting and related scoring rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 399-429, July.
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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. Terzopoulou, Zoi & Endriss, Ulle, 2021. "The Borda class," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 31-40.
    4. Florian Brandl & Dominik Peters, 2019. "An axiomatic characterization of the Borda mean rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(4), pages 685-707, April.
    5. repec:hal:pseose:halshs-01249513 is not listed on IDEAS
    6. 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.
    7. Martin Lackner & Jan Maly, 2020. "Approval-Based Shortlisting," Papers 2005.07094, arXiv.org, revised May 2022.

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    More about this item

    Keywords

    Binary evaluations; judgment aggregation; mean rule; tension; Borda.;
    All these keywords.

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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