Skip to main content
Springer Nature Link
Log in

Which is better: the Condorcet or Borda winner?

  • Original Paper
  • Published:
Social Choice and Welfare Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Notes

  1. Risse [11] and Sanver’s informative 2004 Oberwolfach talk describe Brams and Sanver’s claim that the Approval Voting outcomes of any profile must include all possible positional and many other procedures’ outcomes, maybe even the Condorcet loser, where each outcome in this large set of possibilities can be sincere even if undesired! When I proved this fact in 1988 (Saari and Van Newenhizen [26], see Saari [14, 18] for easy ways to construct all possible AV outcomes for a profile) to demonstrate AV’s chaotic indeterminacy, Brams, Fishburn and Merrill [2] disputed my argument, so I welcome this belated agreement. But while each AV outcome can be sincere (or strategic), it is easy to show that the voters need not like the outcome—with AV, they can elect what they do not want. So Risse’s acceptance of this AV multiple outcome property as “a friendly amendment to my argument for the multiplicity thesis” contributes to my worry about the lack of substance attached to his use of “reasonable”.

  2. “Tiny” here involves a one in 17,001 data change, or even a one in 17,000,001 change.

  3. As an example, let k voters prefer ABC, k prefer BAC and k+1 prefer CAB. Even though C is bottom ranked by \(\frac{{2k}}{{3k + 1}} = \frac{2}{3} - \frac{2}{{9k + 3}}\) of the voters, she is the plurality winner.

  4. Because a candidate’s Borda tally can be found by adding the pairwise tallies she receives against everyone else, the Borda count can be used with cyclic preferences and it cancels them leaving a tie. Sieberg and I [25] used this point to analyze engineering decisions where cyclic data do arise.

References

  1. Arrow K (1951) (2nd ed 1963), Social choice and individual values. Wiley, New York

    MATH  Google Scholar 

  2. Brams S, Fishburn P, Merrill S (1988) The responsiveness of approval voting: comments on Saari and Van Newenhizen. Public Choice 59:121–131

    Article  Google Scholar 

  3. Fishburn P (1981) Inverted orders for monotone scoring rules. Discrete Appl Math 3:27–36

    Article  MATH  MathSciNet  Google Scholar 

  4. Gibbard A (1973) Manipulation of voting schemes: a general result. Econometrica 41:587–601

    MATH  MathSciNet  Google Scholar 

  5. Kemeny J (1959) Mathematics without numbers. Daedalus 88:571–591

    Google Scholar 

  6. Merlin V, Saari DG (2000) Changes that cause changes. Soc Choice Welf 17:691–705

    Article  MathSciNet  MATH  Google Scholar 

  7. Nurmi H (1999) Voting paradoxes and how to deal with them. Springer

  8. Nurmi H (2002) Voting procedures under uncertainty. Springer, Berlin Heidelberg New York

    MATH  Google Scholar 

  9. Ratliff T (2004) Presentation at a Oberwolfach, Germany, conference

  10. Risse M (2001) Arrow’s theorem, indeterminacy, and multiplicity reconsidered. Ethics 111:706–734

    Article  Google Scholar 

  11. Risse M (2004) Why the Count de Borda cannot beat the Marquis de Condorcet, Social Choice and Welfare, this issue

  12. Saari DG (1989) A dictionary for voting paradoxes. J Econ Theory 48:443–475

    Article  MATH  MathSciNet  Google Scholar 

  13. Saari DG (1990) Susceptibility to manipulation. Public Choice 64:21–41

    Article  Google Scholar 

  14. Saari DG (1994) Geometry of voting. Springer, Berlin Heidelberg New York

    MATH  Google Scholar 

  15. Saari DG (1995) A chaotic exploration of aggregation paradoxes. SIAM Rev 37:37–52

    Article  MATH  MathSciNet  Google Scholar 

  16. Saari DG (1999) Explaining all three-alternative voting outcomes. J Econ Theory 87:313–355

    Article  MATH  MathSciNet  Google Scholar 

  17. Saari DG (2000) Mathematical structure of voting paradoxes. Econom Theory 15:1–101

    Article  MATH  MathSciNet  ADS  Google Scholar 

  18. Saari DG (2001) Chaotic elections! A mathematician looks at voting, American Mathematical Society, Providence, R.I.

    MATH  Google Scholar 

  19. Saari DG (2001) Decisions and elections: explaining the unexpected, Cambridge University Press, New York

    MATH  Google Scholar 

  20. Saari DG (2002) Adopting a plurality vote perspective. Math Oper Res 27:45–64

    Article  MATH  MathSciNet  Google Scholar 

  21. Saari DG (2003) Capturing the ‘will of the people.’ Ethics 113:333–334

    Article  Google Scholar 

  22. Saari DG (2003) Disturbing aspects of voting theory. Econ Theory 22:529–556

    Article  MATH  MathSciNet  Google Scholar 

  23. Saari DG, Merlin V (2000) A geometric examination of Kemeny’s rule. Soc Choice Welf 17:403–438

    Article  MathSciNet  MATH  Google Scholar 

  24. Saari DG, Sieberg K (2001) The sum of the parts can violate the whole. Am Polit Sci Rev 95:415–430

    Article  Google Scholar 

  25. Saari DG, Sieberg K (2004) Are part wise comparisons reliable? Res Eng Des 15:62–71

    Article  Google Scholar 

  26. Saari DG, Van Newenhizen J (1988) Is approval voting an “unmitigated evil?” Public Choice 59:133–147

    Article  Google Scholar 

  27. Satterthwaite M (1975) Strategy proofness and Arrow’s conditions. J Econ Theory 10:187–217

    Article  MATH  MathSciNet  Google Scholar 

  28. Sen A (1970) Collective choice and social welfare. Holden Day, San Francisco

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Mathematical Behavioral Sciences, University of California, Irvine, CA, 92697-5100, USA

    Donald G. Saari

Authors
  1. Donald G. Saari
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Donald G. Saari.

Additional information

This research was supported by an NSF DMI grant. While this paper addresses Risse’s [11] paper, it is based on my 3/10/04 presentation at a 2004 Oberwolfach meeting on the design of electoral systems. My thanks to the organizers M. Balinski, S. Brams, and F. Pukelsheim

Rights and permissions

Reprints and permissions

About this article

Cite this article

Saari, D.G. Which is better: the Condorcet or Borda winner?. Soc Choice Welfare 26, 107–129 (2006). https://doi.org/10.1007/s00355-005-0046-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00355-005-0046-2

Keywords