More Than Two Alternatives

  • Adiel Teixeira de AlmeidaEmail author
  • Danielle Costa Morais
  • Hannu Nurmi
Part of the Advances in Group Decision and Negotiation book series (AGDN, volume 9)


We introduce and discuss the most common voting procedures. Our starting point is the observation that voting rules can make a significant difference in the voting outcomes. First we deal with the ambiguity of the notion of majority outcome in cases involving more than two alternatives or candidates. The concepts of Condorcet winner and core are introduced. We then define the voting procedures and present some descriptive devices for the analysis of voting situations.


  1. Arrow, K. J. (1963). Social choice and individual values, 2nd edn. New Haven: Yale University Press (1st edn. 1951).Google Scholar
  2. Campbell, D. E., & Kelly, J. S. (2003). A strategy-proofness characterization of majority rule. Economic Theory, 22, 557–568.MathSciNetCrossRefGoogle Scholar
  3. Campbell, D. E., & Kelly, J. S. (2015). Anonymous, neutral and strategy-proof rules on the Condorcet domain. Economics Letters, 128, 79–82.MathSciNetCrossRefGoogle Scholar
  4. Dasgupta, P., & Maskin, E. (2008). On the robustness of majority rule. Journal of the European Economic Association, 6, 949–973.CrossRefGoogle Scholar
  5. Felsenthal, D., & Machover, M. (1992). After two centuries, should Condorcet’s voting procedure be implemented? Behavioral Science, 37, 250–274.CrossRefGoogle Scholar
  6. Felsenthal, D., & Nurmi, H. (2018). Voting procedures for electing a single candidate. Proving Their (In)Vulnerability to Various Voting Paradoxes, Cham: Springer.Google Scholar
  7. Fishburn, P. C. (1973). The theory of social choice. Princeton: Princeton University Press.zbMATHGoogle Scholar
  8. Gärdenfors, P. (1976). Manipulation of social choice functions. Journal of Economic Theory, 13, 217–228.MathSciNetCrossRefGoogle Scholar
  9. McLean, I. (1991). Forms of representation and systems of voting. In D. Held (Ed.), Political theory today. Cambridge: Polity Press.Google Scholar
  10. Merrill, L. (2011). Parity dependence of a majority rule characterization on the Condorcet domain. Economics Letters, 112, 259–261.MathSciNetCrossRefGoogle Scholar
  11. Nurmi, H. (1987). Comparing voting systems. Dordrecht: D. Reidel.CrossRefGoogle Scholar
  12. Pattanaik, P. K. (2003). Positional rules of collective decision making. In K. J. Arrow, A. K. Sen, & K. Suzumura (Eds.), Handbook of social choice and welfare (Vol. I, pp. 361–394). Amsterdam: North-Holland.Google Scholar
  13. Risse, M. (2001). Arrow’s theorem, indeterminacy and multiplicity reconsidered. Ethics, 111, 706–734.CrossRefGoogle Scholar
  14. Saari, D. G. (1995). Basic geometry of voting. Berlin-Heidelberg: Springer.CrossRefGoogle Scholar
  15. Saari, D. (2003). Capturing the “Will of the People”. Ethics, 113, 333–349.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Universidade Federal de Pernambuco (UFPE)RecifeBrazil
  2. 2.University of TurkuTurkuFinland

Personalised recommendations