The (In)Vulnerability of 20 Voting Procedures to Lack of Monotonicity in a Restricted Domain

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


This chapter focuses on the possibility that some well-known voting procedures lead to specific types of monotonicity paradoxes in preference profiles that are characterized by the presence and election of a Condorcet winner. Moulin’s (Journal of Economic Theory 45:53–64, 1988) theorem establishes the incompatibility of Condorcet-consistency and invulnerability to the No-Show paradox in voting procedures when there are more than three alternatives to be chosen from. We ask whether this conclusion would also hold in the proper subset of profiles distinguished by the property that a Condorcet winner exists and is elected in the initial profile. Our focus is on 20 voting procedures designed to elect a single candidate. These procedures include both Condorcet-consistent and non-consistent rules. The former are, however, only briefly touched upon because their invulnerability to most types of monotonicity violations in the restricted domain is obvious.


Elections Non-monotonicity No-show paradox Condorcet-consistency Fixed electorates Variable electorates 


  1. Bartholdi, J. J., Tovey, C. A., & Trick, M. A. (1989). The computational difficulty of manipulating an election. Social Choice and Welfare, 6, 227–241.CrossRefGoogle Scholar
  2. 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 (pp. 19–91). Heidelberg: Springer.CrossRefGoogle Scholar
  3. Felsenthal, D. S., & Machover, M. (2008). The majority judgment voting procedure: A critical evaluation. Homo Oeconomicus, 25, 319–333.Google Scholar
  4. Felsenthal, D. S., & Maoz, Z. (1992). Normative properties of four single-stage multi-winner electoral procedures. Behavioral Science, 37, 109–127.CrossRefGoogle Scholar
  5. Felsenthal, D. S., & Nurmi, H. (2016). Two types of participation failure under nine voting methods in variable electorates. Public Choice, 168, 115–135.CrossRefGoogle Scholar
  6. Felsenthal, D. S., & Nurmi, H. (2017). Monotonicity failures afflicting procedures for electing a single candidate. Cham, Switzerland: Springer.CrossRefGoogle Scholar
  7. Felsenthal, D. S., & Nurmi, H. (2018). Voting procedures for electing a single candidate: Proving their (in)vulnerability to various voting paradoxes. Cham, Switzerland: Springer.CrossRefGoogle Scholar
  8. Felsenthal, D. S., & Tideman, N. (2013). Varieties of failure of monotonicity and participation under five voting methods. Theory and Decision, 75, 59–77.CrossRefGoogle Scholar
  9. Felsenthal, D. S., & Tideman, N. (2014). Interacting double monotonicity failure with direction of impact under five voting methods. Mathematical Social Sciences, 67, 57–66.Google Scholar
  10. Fishburn, P. C. (1982). Monotonicity paradoxes in the theory of elections. Discrete Applied Mathematics, 4, 119–134.CrossRefGoogle Scholar
  11. Fishburn, P. C., & Brams, S. J. (1983). Paradoxes of preferential voting. Mathematics Magazine, 56, 207–214.CrossRefGoogle Scholar
  12. Gibbard, A. (1973). Manipulation of voting systems: A general result. Econometrica, 41, 587–601.CrossRefGoogle Scholar
  13. Maskin, E. (1999). Nash equilibrium and welfare optimality. Review of Economic Studies, 66, 23–38.CrossRefGoogle Scholar
  14. Meredith, J. C. (1913). Proportional representation in Ireland. Dublin: Edward Ponsonby, Ltd. (Reprint from the collection of the University of California Libraries).Google Scholar
  15. Miller, N. R. (2017). Closeness matters: Monotonicity failure in IRV elections with three candidates. Public Choice, 173, 91–108.CrossRefGoogle Scholar
  16. Moulin, H. (1988). Condorcet’s principle implies the no-show paradox. Journal of Economic Theory, 45, 53–64.CrossRefGoogle Scholar
  17. Nurmi, H. (2004). Monotonicity and its cognates in the theory of choice. Public Choice, 121, 25–49.CrossRefGoogle Scholar
  18. Pérez, J. (2001). The strong no show paradoxes are a common flaw in Condorcet voting correspondences. Social Choice and Welfare, 18, 601–616.CrossRefGoogle Scholar
  19. Satterthwaite, M. A. (1975). Strategy-proofness and Arrow’s conditions: Existence and correspondence theorems for voting procedures and social choice functions. Journal of Economic Theory, 10, 187–217.CrossRefGoogle Scholar
  20. Slinko, A., & White, S. (2014). Is it ever safe to vote strategically? Social Choice and Welfare, 43, 403–427.CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of Philosophy, Contemporary History and Political ScienceUniversity of TurkuTurkuFinland

Personalised recommendations