20 Voting Procedures Designed to Elect a Single Candidate

  • Dan S. Felsenthal
  • Hannu NurmiEmail author
Part of the SpringerBriefs in Economics book series (BRIEFSECONOMICS)


20 voting procedures for electing a single candidate are introduced and briefly commented upon. The procedures fall into three classes in terms of the type of voter input and Condorcet consistency: non-ranked procedures, ranked procedures that are not Condorcet-consistent and ranked ones that are Condorcet-consistent. The first class consists of four procedures, the second consists of seven procedures and the third class consists of nine procedures.


Non-ranked voting procedures Ranked procedures Condorcet-consistent procedures 


  1. Baldwin, J. M. (1926). The technique of the Nanson preferential majority system. Proceedings of the Royal Society of Victoria, 39, 42–52.Google Scholar
  2. Balinski, M., & Laraki, R. (2007a). A theory of measuring, electing and ranking. Proceedings of the National Academy of Sciences of the United States of America (PNAS), 104, 8720–8725.Google Scholar
  3. Balinski, M., & Laraki, R. (2007b). Election by majority judgement: Experimental evidence, (mimeograph). Paris: Ecole Polytechnique, Centre National De La Recherche Scientifique, Laboratoire D’Econometrie, Cahier No. 2007–28. Downloadable from
  4. Balinski, M., & Laraki, R. (2011). Majority judgment: Measuring, ranking, and electing. Cambridge, MA: MIT Press.CrossRefGoogle Scholar
  5. Black, D. (1958). The theory of committees and elections. Cambridge: Cambridge University Press.Google Scholar
  6. Brams, S. J., & Fishburn, P. C. (1978). Approval voting. American Political Science Review, 72, 831–847.CrossRefGoogle Scholar
  7. Brams, S. J., & Fishburn, P. C. (1983). Approval voting. Boston: Birkhäuser.Google Scholar
  8. Coombs, C. H. (1964). A theory of data. New York: Wiley.Google Scholar
  9. Coombs, C. H., Cohen, J. L., & Chamberlin, J. R. (1984). An empirical study of some election systems. American Psychologist, 39, 140–157.CrossRefGoogle Scholar
  10. Copeland, A. H. (1951). A ‘reasonable’ social welfare function, mimeographed. University of Michigan, Department of Mathematics, Seminar on Applications of Mathematics to the Social Sciences.Google Scholar
  11. de Borda, J.-C. (1784) [1995]. Mémoire sur les élections au scrutin. Histoire de l’Academie Royale des Sciences année 1781 (pp. 651–665). Paris. Reprinted and translated in I. McLean & A. B. Urken (1995), Classics of social choice (pp. 83–89). Ann Arbor, MI: University of Michigan Press.Google Scholar
  12. Farquharson, R. (1969). Theory of voting. New Haven, CT: Yale University Press.Google Scholar
  13. Felsenthal, D. S. (2012). Review of paradoxes afflicting procedures for electing a single candidate. In D. S. Felsenthal & M. Machover (Eds.), Electoral systems: Paradoxes, assumptions, and procedures (Ch. 3, pp. 19–92). Berlin Heidelberg: Springer.Google Scholar
  14. Felsenthal, D. S., & Machover, M. (1992). After two centuries should Condorcet’s voting procedure be implemented? Behavioral Science, 37, 250–273.CrossRefGoogle Scholar
  15. Felsenthal, D. S., & Nurmi, H. (2018). Voting procedures for electing a single candidate—Proving their (in)vulnerability to various voting procedures. Cham, Switzerland: Springer.CrossRefGoogle Scholar
  16. Fishburn, P. C. (1977). Condorcet social choice functions. SIAM Journal on Applied Mathematics, 33, 469–489.CrossRefGoogle Scholar
  17. Hoag, C. G., & Hallett, G. H. (1926). Proportional representation. New York: The Macmillan Co.Google Scholar
  18. Kemeny, J. G. (1959). Mathematics without numbers. Daedalus, 88, 577–591.Google Scholar
  19. Kemeny, J. G., & Snell, J. L. (1960). Mathematical models in the social sciences. Boston: Ginn.Google Scholar
  20. Kramer, G. H. (1977). A dynamical model of political equilibrium. Journal of Economic Theory, 16, 310–333.CrossRefGoogle Scholar
  21. Lepelley, D., Moyouwou, I., & Smaoui, H. (2018). Monotonicity paradoxes in three-candidate elections using scoring elimination rules. Social Choice and Welfare, 50, 1–33.CrossRefGoogle Scholar
  22. McLean, I., & Urken, A. B. (1995). Classics of social choice. Ann Arbor: University of Michigan Press.CrossRefGoogle Scholar
  23. Nanson, E. J. (1883). Methods of elections. Transactions and Proceedings of the Royal Society of Victoria, 19, 197–240. Also in I. McLean & A. B. Urken (Eds.), Classics of social choice (Ch. 14, pp. 321–359, 1995). University of Michigan Press.Google Scholar
  24. Niou, E. M. S. (1987). A note on Nanson’s rule. Public Choice, 54, 191–193.CrossRefGoogle Scholar
  25. Nurmi, H. (1989). On Nanson’s method. In O. Borg, O. Apunen, H. Hakovirta, & J. Paastela (Eds.), Democracy in the modern world. Essays for Tatu Vanhanen, series A (Vol. 260, pp. 199–210). Tampere: Acta Universitatis Tamperensis.Google Scholar
  26. Schultze, M. (2003). A new monotonic and clone-independent single-winner election method. Voting Counts, 17, 9–19. Downloadable from:
  27. Schwartz, T. (1972). Rationality and the myth of the maximum. Noûs, 6, 97–117.CrossRefGoogle Scholar
  28. Schwartz, T. (1986). The logic of collective choice. New York: Columbia University Press.Google Scholar
  29. Simpson, P. B. (1969). On defining areas of voter choice: Professor Tullock on stable voting. Quarterly Journal of Economics, 83, 478–490.CrossRefGoogle Scholar
  30. Smith, W. D. (2000). Range voting. Downloadable from:
  31. Straffin, P. D. (1980). Topics in the theory of voting. Boston: Birkhäuser.Google Scholar
  32. Tideman, T. N. (1987). Independence of clones as a criterion for voting rules. Social Choice and Welfare, 4, 185–206.CrossRefGoogle Scholar
  33. Tideman, N. (2006). Collective decisions and voting: The potential for public choice. Aldershot, Hampshire, England: Ashgate Publishing Ltd.Google Scholar
  34. Young, H. P. (1977). Extending Condorcet’s rule. Journal of Economic Theory, 16, 335–353.CrossRefGoogle Scholar
  35. Young, H. P. (1988). Condorcet’s theory of voting. American Political Science Review, 82, 1231–1244.CrossRefGoogle Scholar
  36. Young, H. P. (1995). Optimal voting rules. Journal of Economic Perspectives, 9, 51–63.CrossRefGoogle Scholar
  37. Young, H. P., & Levenglick, A. (1978). A consistent extension of Condorcet’s election principle. SIAM Journal of Applied Mathematics, 35, 283–300.CrossRefGoogle Scholar

Copyright information

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Political SciencesUniversity of HaifaHaifaIsrael
  2. 2.Department of Philosophy, Contemporary History and Political ScienceUniversity of TurkuTurkuFinland

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