Other Voting Rules and Considerations

  • William V. Gehrlein
  • Dominique Lepelley
Part of the Studies in Choice and Welfare book series (WELFARE)


Commonly studied voting rules are thoroughly evaluated on the basis of the probability that their election outcomes can be manipulated with insincere voting, since it is a frequently held belief that Borda Rule is particularly susceptible to manipulation. A careful investigation shows that the validity of this perception does not hold up under scrutiny. A voting rule that has recently received a lot of attention is also analyzed; the Three-valued Scale Evaluative Voting Procedure that can be viewed either as a particular case of Range Voting or as an extension of Approval Voting. The case of more than three candidates is considered to determine if the overall superiority of Borda Rule remains valid, and the significant impact of voter abstention on election outcomes is investigated.


  1. Alcantud, J. C., & Laruelle, A. (2014). Dis&approval voting: A characterization. Social Choice and Welfare, 43, 1–10.CrossRefGoogle Scholar
  2. Aleskerov, F., Ivanov, A., Karabekyan, D., & Yakuba, V. (2015). Manipulability of aggregation procedures in impartial anonymous culture. Procedia Computer Science, 55, 1250–1257.CrossRefGoogle Scholar
  3. Aleskerov, F., Karabekyan, D., Sanver, R., & Yakuba, V. (2011). On individual manipulability of positional voting rules. SERIEs: Journal of the Spanish Economic Association, 2, 431–446.CrossRefGoogle Scholar
  4. Aleskerov, F., Karabekyan, D., Sanver, R., & Yakuba, V. (2012). On the manipulability of voting rules: Case of 4 and 5 alternatives. Mathematical Social Sciences, 64, 67–73.CrossRefGoogle Scholar
  5. Baharad, E., & Neeman, Z. (2002). The asymptotic strategyproofness of scoring and Condorcet consistent rules. Review of Economic Design, 7, 331–340.CrossRefGoogle Scholar
  6. Béhue, V., Favardin, P., & Lepelley, D. (2009). La manipulation stratégique des règles de vote: Une étude expérimentale. Louvain Economic Review, 75, 503–516.Google Scholar
  7. Black, D. (1958). The theory of committees and elections. Cambridge: Cambridge University Press.Google Scholar
  8. Blais, A. (2002). Why is there so little strategic voting in Canadian Plurality Rule elections? Political Studies, 50, 445–454.CrossRefGoogle Scholar
  9. Bruns, W., Ichim, B., & Söger, C. (2017). Computations of volumes and Ehrhart series in four candidate elections. Working Paper at
  10. Chamberlin, J. R. (1985). An investigation into the relative manipulability of four voting systems. Behavioral Science, 30, 195–203.CrossRefGoogle Scholar
  11. de Condorcet, M. (1793). A survey of the principles underlying the Draft Constitution presented to the National Convention on 15th and 16th February 1793. In F. Sommerlad, I. McLean (Eds., 1989), The political theory of Condorcet (pp. 216–222). Oxford: University of Oxford Working Paper.Google Scholar
  12. DeSilver, D. (2016). US voter turnout trails most developed countries. Pew Research Center Report:
  13. El Ouafdi, A., Lepelley, D., & Smaoui, H. (2017a). On the Condorcet Efficiency of evaluative voting (and other voting rules) with trichotomous preferences. University of La Réunion, Working Paper.Google Scholar
  14. El Ouafdi, A., Lepelley, D., & Smaoui, H. (2017b). Probabilities of electoral outcomes in four-candidate elections. University of La Réunion, Working Paper.Google Scholar
  15. Favardin, P., & Lepelley, D. (2006). Some further results on the manipulability of social choice rules. Social Choice and Welfare, 26, 485–509.CrossRefGoogle Scholar
  16. Favardin, P., Lepelley, D., & Serais, J. (2002). Borda Rule, Copeland method and strategic manipulation. Review of Economic Design, 7, 213–228.CrossRefGoogle Scholar
  17. Felsenthal, D. (2012). Review of paradoxes afflicting procedures for electing a single candidate. In S. Dan Felsenthal, & M. Machover(Ed.), Electoral systems: Paradoxes, assumptions and procedures (pp. 19–92). Berlin: Springer.CrossRefGoogle Scholar
  18. Gehrlein, W., & Lepelley, D. (2017). The impact of abstentions on election outcomes when voters have dependent preferences. Technical Note available on Research Gate at:
  19. Gehrlein, W. V., & Fishburn, P. C. (1978). Probabilities of election outcomes for large electorates. Journal of Economic Theory, 19, 38–49.CrossRefGoogle Scholar
  20. Gehrlein, W. V., & Fishburn, P. C. (1979). Effects of abstentions on voting procedures in three-candidate elections. Behavioral Science, 24, 346–354.CrossRefGoogle Scholar
  21. Gibbard, A. (1973). Manipulation of voting schemes: A general result. Econometrica, 41, 587–601.CrossRefGoogle Scholar
  22. Kube, S., & Puppe, C. (2009). When and how do voters try to manipulate? Experimental evidence from Borda elections. Public Choice, 139, 39–52.CrossRefGoogle Scholar
  23. Laslier, J. F. (2010). In silico voting experiments. In J. F. Laslier & R. Sanver (Eds.), Handbook of approval voting. Berlin: Springer.CrossRefGoogle Scholar
  24. Lehtinen, A. (2007). The Borda rule is also intended for dishonest men. Public Choice, 133, 73–90.CrossRefGoogle Scholar
  25. Lepelley, D., Louichi, A., & Valognes, F. (2000). Computer simulations of voting systems. In G. Ballot & G. Weisbuch (Eds.), Applications of simulations to social sciences. Oxford: Hermes.Google Scholar
  26. Lepelley, D., & Mbih, B. (1987). The proportion of coalitionally unstable situations under the plurality rule. Economics Letters, 24, 311–315.CrossRefGoogle Scholar
  27. Lepelley, D., & Mbih, B. (1994). The vulnerability of four social choice functions to coalitional manipulation of preferences. Social Choice and Welfare, 11, 253–265.CrossRefGoogle Scholar
  28. Lhuilier, S. (1794). An examination of the election method proposed to the National Convention of France in February 1793, and Adopted in Geneva. In F. Sommerlad, & I. McLean (Eds., 1989), The political theory of Condorcet (pp. 223–253). Oxford: University of Oxford Working Paper.Google Scholar
  29. Milner, H., Loewen, P. J., & Hicks, B. M. (2007). The paradox of compulsory voting: Participation does not equal political knowledge. IRPP Policy Matters, 8. Available at:
  30. Moyouwou, I., & Tchantcho, H. (2017). Asymptotic vulnerability of positional voting rules to coalitional manipulation. Mathematical Social Sciences, 89, 70–82.Google Scholar
  31. Nitzan, S. (1985). The vulnerability of point-voting schemes to preference variation and strategic manipulation. Public Choice, 47, 349–370.CrossRefGoogle Scholar
  32. Peleg, B. (1979). A note on manipulability of large voting schemes. Theory and Decision, 11, 401–412.CrossRefGoogle Scholar
  33. Pritchard, G., & Slinko, A. (2006). On the average minimum size of a manipulating coalition. Social Choice and Welfare, 27, 263–277.CrossRefGoogle Scholar
  34. Pritchard, G., & Wilson, M. C. (2007). Exact results on manipulability of positional voting rules. Social Choice and Welfare, 29, 487–513.CrossRefGoogle Scholar
  35. Saari, D. G. (1990). Susceptibility to manipulation. Public Choice, 64, 21–41.CrossRefGoogle Scholar
  36. Satterthwaite, M. (1975). Strategy-proofness and arrow’s condition. Journal of Economic Theory, 10, 198–217.CrossRefGoogle Scholar
  37. Schürmann, A. (2013). Exploiting polyhedral symmetries in social choice. Social Choice and Welfare, 40, 1097–1110.CrossRefGoogle Scholar
  38. Slinko, A. (2002). On asymptotic strategy-proofness of classical social choice rules. Theory and Decision, 52, 389–398.CrossRefGoogle Scholar
  39. Smaoui, H., & Lepelley, D. (2013). Le système de vote par note à trois niveaux: étude d’un nouveau mode de scrutin. Revue d’Economie Politique, 123, 827–850.CrossRefGoogle Scholar
  40. Smith, D. A. (1999). Manipulability measures of common social choice functions. Social Choice and Welfare, 16, 639–661.CrossRefGoogle Scholar
  41. Wilson, M. C., & Pritchard, G. (2007). Probability calculations under the IAC hypothesis. Mathematical Social Sciences, 54, 244–256.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • William V. Gehrlein
    • 1
  • Dominique Lepelley
    • 2
  1. 1.Department of Business AdministrationUniversity of DelawareNewarkUSA
  2. 2.University of La RéunionSaint-Denis, Ile de La RéunionFrance

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