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The Borda rule and the pairwise-majority-loser revisited

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  • Noriaki Okamoto

    (Keio University)

  • Toyotaka Sakai

    (Keio University)

Abstract

Jean-Charles de Borda introduced the Borda rule with the motivation of avoiding the so-called pairwise-majority-loser. We revisit this topic by examining the uniqueness of the Borda rule as a scoring rule that is consistent with the pairwise-majority-loser criterion. We first show that this uniqueness does not hold for any fixed population. In fact, when there are three alternatives and six voters, all scoring rules are consistent with the pairwise-majority-loser criterion. We then show that for each non-Borda scoring rule, there exists a population n such that the rule is not consistent with this criterion for all populations of size larger than n.

Suggested Citation

  • Noriaki Okamoto & Toyotaka Sakai, 2019. "The Borda rule and the pairwise-majority-loser revisited," Review of Economic Design, Springer;Society for Economic Design, vol. 23(1), pages 75-89, June.
    • Handle: RePEc:spr:reecde:v:23:y:2019:i:1:d:10.1007_s10058-019-00221-3
    DOI: 10.1007/s10058-019-00221-3
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    References listed on IDEAS

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    1. Saari, Donald G., 1999. "Explaining All Three-Alternative Voting Outcomes," Journal of Economic Theory, Elsevier, vol. 87(2), pages 313-355, August.
    2. Fishburn, Peter C., 1974. "Paradoxes of Voting," American Political Science Review, Cambridge University Press, vol. 68(2), pages 537-546, June.
    3. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    4. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521516051, January.
    5. Saari, Donald G., 1989. "A dictionary for voting paradoxes," Journal of Economic Theory, Elsevier, vol. 48(2), pages 443-475, August.
    6. K. J. Arrow & A. K. Sen & K. Suzumura (ed.), 2002. "Handbook of Social Choice and Welfare," Handbook of Social Choice and Welfare, Elsevier, edition 1, volume 1, number 1.
    7. Pattanaik, Prasanta K., 2002. "Positional rules of collective decision-making," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 7, pages 361-394, Elsevier.
    8. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521731607, January.
    9. William V. Gehrlein, 2006. "Condorcet’s Paradox," Theory and Decision Library C, Springer, number 978-3-540-33799-7, December.
    10. 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.
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    Cited by:

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