Abstract
This note lists the most well-known paradoxes (or pathologies) which may afflict voting procedures designed to elect one out of several candidates and calls for future research to focus on finding the necessary and/or sufficient conditions for these paradoxes to occur under various voting procedures in order to be able to better assess the likelihood of occurrence of these paradoxes under these procedures.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The relevant data include, inter alia, the number of voters, the number of candidates, the number of candidates that must be elected, the preference ordering of every voter among the competing candidates, the amount of information voters have regarding all other voters’ preference orderings, the order in which voters cast their votes if it is not simultaneous, the order in which candidates are voted upon if candidates are not voted upon simultaneously, whether voting is open or secret and the manner in which ties are to be broken.
- 2.
This procedure is also known as Instant Runoff Voting (IRV), Hare rule, or Ranked Choice Voting. According to this procedure voters rank the candidates in order of preference. A candidate supported by a majority of first preferences is elected. Otherwise the candidate supported by the fewest first preferences is eliminated and his or her ballots are transferred to other candidates on the basis of second preferences. This process is repeated until one candidate is supported by a majority of ballots.
References
Aizerman, M. A., & Malishevsky, A. V. (1981). General theory of best variants choice: Some aspects. IEEE Transactions on Automatic Control AC–26, 1030–1040.
Black, D. (1958). The theory of committees and elections. Cambridge: Cambridge University Press.
Borda, J.–C. de (1784) [1995]. Mémoire sur les élections au scrutin, Histoire de l’Academie Royaledes Sciences année 1781, pp. 651–665. Paris. Reprinted and translated in I. McLean and A. B. Urken (1995), Classics of social choice, Ann Arbor, MI: University of Michigan Press, pp. 83–89.
Brams, S. J. (1982). The AMS nominating system is vulnerable to truncation of preferences. Notices of the American Mathematical Society, 29, 136–138.
Chernoff, H. (1954). Rational selection of decision functions. Econometrica, 22, 422–443.
de Condorcet, Marquis. (1785). Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix. Paris: L’Imprimerie Royale.
Farquharson, R. (1969). Theory of voting. New Haven, CT: Yale University Press.
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.
Felsenthal, D. S., & Nurmi, H. (2017). Monotonicity failures afflicting procedures for electing a single candidate. Cham, Switzerland: Springer.
Felsenthal, D. S., & Nurmi, H. (2018). Voting procedures for electing a single candidate: Proving their (in)vulnerability to various voting paradoxes. Cham, Switzerland: Springer.
Fishburn, P. C. (1974a). Paradoxes of voting. American Political Science Review, 68, 537–546.
Fishburn, P. C. (1974b). Social choice functions. SIAM Review, 16, 63–90.
Fishburn, P. C. (1974c). On the sum–of–ranks winner when losers are removed. Discrete Mathematics, 8, 25–30.
Fishburn, P. C. (1974d). Subset choice conditions and the computation of social choice sets. The Quarterly Journal of Economics, 88, 320–329.
Fishburn, P. C. (1977). Condorcet social choice functions. SIAM Journal on Applied Mathematics, 33, 469–489.
Fishburn, P. C., & Brams, S. J. (1983). Paradoxes of preferential voting. Mathematics Magazine, 56, 207–214.
Holzman, R. (1988/89). To vote or not to vote: What is the quota? Discrete Applied Mathematics, 22, 133–141.
Miller, N. R. (2017). Closeness matters: Monotonicity failure in IRV elections with three candidates. Public Choice, 173, 91–108.
Moulin, H. (1988). Condorcet’s principle implies the No–Show paradox. Journal of Economic Theory, 45, 53–64.
Pérez, J. (1995). Incidence of No–Show paradoxes in Condorcet choice functions. Investigaciones Economicas, 19, 139–154.
Saari, D. G., & Barney, S. (2003). Consequences of reversing the preferences. Mathematical Intelligencer, 25, 17–31.
Sen, A. K. (1970). Collective choice and social welfare. San Francisco: Holden-Day.
Smith, J. H. (1973). Aggregation of preferences with variable electorate. Econometrica, 41, 1027–1041.
Young, H. P. (1974). An axiomatization of Borda’s rule. Journal of Economic Theory, 9, 43–52.
Acknowledgements
I wish to thank Felix Brandt and Piotr Faliszewski for their helpful comments.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Felsenthal, D.S. (2019). On Paradoxes Afflicting Voting Procedures: Needed Knowledge Regarding Necessary and/or Sufficient Condition(s) for Their Occurrence. In: Laslier, JF., Moulin, H., Sanver, M., Zwicker, W. (eds) The Future of Economic Design. Studies in Economic Design. Springer, Cham. https://doi.org/10.1007/978-3-030-18050-8_13
Download citation
DOI: https://doi.org/10.1007/978-3-030-18050-8_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-18049-2
Online ISBN: 978-3-030-18050-8
eBook Packages: Economics and FinanceEconomics and Finance (R0)