The prevalence and consequences of ballot truncation in ranked-choice elections


In ranked-choice elections, voters vote by indicating their preference orderings over the candidates. A ballot is truncated when the ordering is incomplete (called partial voting). Sometimes truncation is forced—voters are allowed to rank only a limited number of candidates—but sometimes it is voluntary. During the vote tabulating process, a truncated ballot is exhausted when all of the candidates it ranks have been eliminated. Ballot exhaustion and, therefore ballot truncation, is a concern in single-winner elections when the margin of victory in the final stage is less than the number of exhausted ballots. That concern motivates our study. We review evidence from actual single-winner ranked-choice elections and conclude that voluntary ballot truncation is very common. Moreover, it is difficult to explain strategically. To assess the significance of ballot truncation, we simulate ranked-choice elections with four, five and six candidates, using both spatial and random models of voter preferences. Does truncation change the probability that a Condorcet winner wins the election? Does the winner change as the extent of truncation increases? We find that even small amounts of truncation can alter election outcomes.

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  1. Abate, T. (2013). Irrepressible candidate Lou Filopovich dies at 90. San Leandro Patch, Feb 11, 2013. Retrieved May 27, 2018 from

  2. Article X: Nominations and Elections, Bylaws of the American Psychological Association. Retrieved May 27, 2018 from

  3. Bartholdi, J. J. III, & Orlin, J. B. (1991). Single transferable vote resists strategic voting. Social Choice and Welfare, 8, 341–354.

    Article  Google Scholar 

  4. Baumeister, D., Faliszewski, P., Lang, J., & Rothe, J. (2012). Campaigns for lazy voters: truncated ballots. In Int. conf. on autonomous agents and multiagent systems (AAMAS) (pp. 577–584).

  5. Brams, S. J. (1982). The AMS nominating system is vulnerable to truncation of preferences. Notices of AMS, 29, 136–138.

    Google Scholar 

  6. Burnett, C. M., & Kogan, V. (2015). Ballot (and voter) “exhaustion” under instant runoff voting: An examination of four ranked-choice elections. Electoral Studies, 37, 41–49.

    Article  Google Scholar 

  7. City of San Francisco (2011). City and County of San Francisco Department of Elections, November 8, 2011 Election Summary, Mayor. Retrieved June 14, 2018 from

  8. City of Santa Fe (2018). Election-March 6, 2018 regular municipal election. Retrieved September 2, 2019 from

  9. Columbia Broadcasting System (2010). Cassidy Wins San Leandro Mayor’s Race by 172 votes, November 12, 2010. Retrieved June 14, 2018 from

  10. Conservative Party of Canada (2016). Conservative Party of Canada rules and procedures for the 2016–2017 leadership, March 8, 2016. Retrieved June 19, 2017 from

  11. Elections Ireland (2002). 29th Dáil. Retrieved May 27, 2018 from

  12. Endersby, J. W., & Towle, M. J. (2018). Counting on ranked choice voting: Evidence from American local elections. In American Political Science Association (APSA) conference.

  13. Fishburn, P. C., & Brams, S. J. (1983). Paradoxes of preferential voting. Mathematics Magazine, 56, 207–214.

    Article  Google Scholar 

  14. Fitzsimmons, Z., & Hemaspaandra, E. (2015). Complexity of manipulative actions when voting with ties. In Fourth int. conf. on algorithmic decision making (ADT) (pp. 103–119).

  15. Gehrlein, W. V., Lepelly, D., & Plassmann, F. (2016). Should voters be required to rank candidates in an election? Social Choice and Welfare, 46, 707–747.

    Article  Google Scholar 

  16. Gierzynski, A. Instant runoff voting: An assessment. Retrieved May 27, 2018 from|~vlrs/IRVassessmet.pdf.

  17. Gierzynski, A., Hamilton, W., & Smith, W. D. (2009). Burlington vermont 2009 IRV mayoral election analysis. Retrieved September 2, 2019 from

  18. Grenier, E. (2017). Popular vote numbers reveal wider margin of victory for Andrew Scheer. CBC news online, May 29, 2017. Retrieved April 18, 2018 from

  19. Laslier, J.-F. (2016). Heuristic voting under the alternative vote: The efficiency of “sour grapes” behavior. Homo Oeconomicus: Journal of Behavioral and Institutional Economics, 33, 57–76.

    Article  Google Scholar 

  20. Mattei, N., & Walsh, T. (2013). PrefLib: A library of preference data. In Proceedings of third international conference on algorithmic decision theory (ADT 2013). Lecture notes in artificial intelligence, November 13–15, 2013. Springer. Retrieved January 25, 2018 from

  21. Menon, V., & Larson, K. (2017). Computational aspects of strategic behaviour in elections with top-truncated ballots. Autonomous Agents and Multiagent Systems, 31, 1506–1547.

    Article  Google Scholar 

  22. Miller, N. R. (2017). Closeness matters: Nonmonotonicity failure in IRV election with three candidates. Public Choice, 173, 91–108.

    Article  Google Scholar 

  23. Narodytska, N., & Walsh, T. (2014). The computational impact of partial votes on strategic voting. arXiv:1405.7714.

  24. Nunez, N., & Sanver, M. R. (2017). Revisiting the connection between the no-show paradox and monotonicity. Mathematical Social Sciences, 90, 9–17.

    Article  Google Scholar 

  25. Nurmi, H. (1999). Voting paradoxes and how to deal with them. Berlin: Springer.

    Google Scholar 

  26. O’Neill, J. (2013). Open STV, Currently at Retrieved September 2, 2019.

  27. Ornstein, J. T., & Norman, R. Z. (2013). Frequency of monotonicity failure under Instant Runoff Voting: Estimates based on a spatial model of elections. Public Choice, 161, 1–9.

    Article  Google Scholar 

  28. Plassmann, F., & Tideman, T. N. (2014). How frequently do different voting rules encounter voting paradoxes in three-candidate elections? Social Choice and Welfare, 42, 31–75.

    Article  Google Scholar 

  29. Popov, S., Popova, A., & Regenwetter, M. (2015). Consensus formation in organizations: Hunting for the social choice conundrum in American Psychological Association elections. Decision, 1, 123–146.

    Article  Google Scholar 

  30. Retrieved June 17, 2018 from

  31. Regenwetter, M., Grofman, B., Popova, A., Messner, W., Davis-Stober, C., & Cavagnaro, D. (2009). Behavioural social choice: A status report. Philosophical Transactions of the Royal Society B: Biological Sciences, 364, 833–843.

    Article  Google Scholar 

  32. Regenwetter, M., Kim, A., Kantor, A., & Ho, M.-H. R. (2007). The unexpected empirical consensus among consensus methods. Psychological Science, 18, 629–635.

    Article  Google Scholar 

  33. Richie, R. (2009). Instant runoff voting on election day 2009: Wins, losses, and the long-term trajectory of reform, June 6, 2009. Retrieved June 17, 2018 from

  34. Saari, D. G. (2000). Mathematical structure of voting paradoxes. Economic Theory, 15, 55–102.

    Article  Google Scholar 

  35. Simonich, M. (2018). Vote for the best; skip the rest. Santa Fe New Mexican, January 11, 2018.

  36. Sweeny, J. (2010). San Leandro mayor facing five challengers. The Mercury News, October 6, 2010. Retrieved May 27, 2018 from

  37. Tessier, C., & Blanchet, A. (2018). Ballot order in cueless elections: A comparison of provincial and municipal elections in Québec. Canadian Journal of Political Science, 51, 83–102.

    Article  Google Scholar 

  38. Vote Different Santa Fe! Our new ranked-choice ballot. Retrieved April 22, 2018 from

  39. Woodall, D. R. (1987). An impossibility theorem for electoral systems. Discrete Mathematics, 66, 209–211.

    Article  Google Scholar 

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Work supported by the Canadian Tri-Council Research Support Fund. The authors were supported by their own individual Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grants (Grant Nos. 5023, 155957-2012, 2015-06126).

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Correspondence to Angèle M. Foley.

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A.M. Foley: formerly Hamel.

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Kilgour, D.M., Grégoire, J. & Foley, A.M. The prevalence and consequences of ballot truncation in ranked-choice elections. Public Choice 184, 197–218 (2020).

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  • Ranked-choice selection
  • Single-winner
  • Ballot truncation
  • Ballot exhaustion

JEL Classification

  • D72
  • K16