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Pairwise consensus and the Borda rule

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  • Mahajne, Muhammad
  • Volij, Oscar

Abstract

We say that a preference profile exhibits pairwise consensus around some fixed preference relation, if whenever a preference relation is closer to it than another one, the Kemeny distance of the profile to the former is not greater than its distance to the latter. We show that if a preference profile exhibits pairwise consensus around a preference relation, then this preference relation coincides with the binary relation induced by the Borda count. We also show that no other scoring rule always selects the top ranked alternative of the preference relation around which there is consensus when such consensus exists.

Suggested Citation

  • Mahajne, Muhammad & Volij, Oscar, 2022. "Pairwise consensus and the Borda rule," Mathematical Social Sciences, Elsevier, vol. 116(C), pages 17-21.
    • Handle: RePEc:eee:matsoc:v:116:y:2022:i:c:p:17-21
    DOI: 10.1016/j.mathsocsci.2021.12.001
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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. Pavel Yu. Chebotarev & Elena Shamis, 1998. "Characterizations of scoring methodsfor preference aggregation," Annals of Operations Research, Springer, vol. 80(0), pages 299-332, January.
    3. Muhammad Mahajne & Shmuel Nitzan & Oscar Volij, 2015. "Level $$r$$ r consensus and stable social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 805-817, December.
    4. Can, Burak & Storcken, Ton, 2013. "Update monotone preference rules," Mathematical Social Sciences, Elsevier, vol. 65(2), pages 136-149.
    5. Donald Saari, 2006. "Which is better: the Condorcet or Borda winner?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(1), pages 107-129, January.
    6. Donald G. Saari & Vincent R. Merlin, 2000. "A geometric examination of Kemeny's rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(3), pages 403-438.
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    Cited by:

    1. Pedro García-del-Valle-y-Durán & Eduardo Gamaliel Hernandez-Martinez & Guillermo Fernández-Anaya, 2022. "The Greatest Common Decision Maker: A Novel Conflict and Consensus Analysis Compared with Other Voting Procedures," Mathematics, MDPI, vol. 10(20), pages 1-39, October.

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