Review of Economic Design

, Volume 23, Issue 1–2, pp 75–89 | Cite as

The Borda rule and the pairwise-majority-loser revisited

  • Noriaki OkamotoEmail author
  • Toyotaka Sakai
Original Paper


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.


Borda rule Social choice Pairwise-majority-loser Scoring rule Condorcet criterion 

JEL Classifiaction

D71 D63 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of EconomicsKeio UniversityTokyoJapan

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