Abstract
In voting theory, monotonicity is the axiom that an improvement in the ranking of a candidate by voters cannot cause a candidate who would otherwise win to lose. The participation axiom states that the sincere report of a voter’s preferences cannot cause an outcome that the voter regards as less attractive than the one that would result from the voter’s non-participation. This article identifies three binary distinctions in the types of circumstances in which failures of monotonicity or participation can occur. Two of the three distinctions apply to monotonicity, while one of those and the third apply to participation. The distinction that is unique to monotonicity is whether the voters whose changed rankings demonstrate non-monotonicity are better off or worse off. The distinction that is unique to participation is whether the marginally participating voter causes his first choice to lose or his last choice to win. The overlapping distinction is whether the profile of voters’ rankings has a Condorcet winner or a cycle at the top. This article traces the occurrence of all of the resulting combination of characteristics in the voting methods that can exhibit failures of monotonicity.
Similar content being viewed by others
References
Black D. (1958) The theory of committees and elections. Cambridge University Press, Cambridge
Campbell D. E., Kelly J. S. (2002) Non-monotonicity does not imply the no-show paradox. Social Choice and Welfare 19: 513–515
Coombs C. H. (1964) A theory of data. Wiley, New York
Coombs C. H., Cohen J. L., Chamberlin J. R. (1984) An empirical study of some election systems. American Psychologist 39: 140–157
Felsenthal D. S., Maoz Z. (1992) Normative properties of four single-stage multi-winner electroral procedures. Behavioral Science 37: 109–127
Fishburn P. C. (1977) Condorcet social choice functions. SIAM Journal of Applied Mathematics 33: 469–489
Fishburn P. C. (1982) Monotonicity paradoxes in the theory of voting. Discrete Applied Mathematics 4: 119–134
Fishburn P. C., Brams S. J. (1983) Paradoxes of preferential voting. Mathematics Magazine 56: 207–214
Gierzynski, A., Hamilton, W., & Smith, W. (2009). Burlington Vermont 2009 IRV mayor election: Thwarted-majority, non-monotonicity & other failures (oops). Range Voting Organization. Accessed August 23, 2011, from http://rangevoting.org/Burlington.html.
McLean, I. & Urken, A. B. (Eds. & trans). (1995). Classics of social choice. Ann Arbor: University of Michigan Press.
Miller, R. N. (2012). Monotonicity failure in IRV elections with three candidates. Paper presented at the world meeting of the public choice societies, Miami, March 8–12, 2012. Accessed March 15, 2012, from http://userpages.umbc.edu/~nmiller/MF&IRV.pdf.
Moulin H. (1988) Condorcet’s principle implies the no show paradox. Journal of Economic Theory 45: 53–64
Nanson, E. J. (1883). Methods of elections. Transactions and Proceedings of the Royal Society of Victoria, 19, 197–240. In I. McLean & A. B. Urken (Eds. & trans), Classics of social choice (pp. 321–359). Ann Arbor: University of Michigan Press, 1995.
Nurmi H. (1999) Voting paradoxes and how to deal with them. Springer, Heidelberg
Potthoff R. F. (2011) Condorcet polling. Public Choice 148: 67–86
Smith, W. D. (2007). The Irish 1990 presidential election, won by Mary Robinson: ”Success” or “failure” for instant runoff voting (ITV)? Range Voting Organization. Accessed August 23, 2011, from http://rangevoting.org/Ireland1990.html.
Straffin P. D. (1980) Topics in the theory of voting. Birkhäuser, Boston
Woodall D. R. (1997) Monotonicity of single-seat preferential election methods. Discrete Applied Mathematics 77: 81–98
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Felsenthal, D.S., Tideman, N. Varieties of failure of monotonicity and participation under five voting methods. Theory Decis 75, 59–77 (2013). https://doi.org/10.1007/s11238-012-9306-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11238-012-9306-7
Keywords
- Elections
- Non-monotonicity
- Participation
- Strategic voting
- Voting paradoxes
- Voting methods
- Voting procedures