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Narrowing the field in elections: The Next-Two rule

Author

Listed:
  • Steven J Brams

    (Department of Politics, New York University, New York, USA)

  • D Marc Kilgour

    (Department of Mathematics, Wilfrid Laurier University, Waterloo, Canada)

Abstract

We suggest a new approach to narrowing the field in elections, based on the ‘deservingness’ of candidates to be contenders in a runoff, or to be declared one of several winners. Instead of specifying some minimum percentage (e.g., 50) that the leading candidate must surpass to avoid a runoff (usually between the top two candidates), we propose that the number of contenders depends on the distribution of votes among all candidates. Divisor methods of apportionment proposed by Jefferson and Webster, among others, provide measures of deservingness, but they can prescribe a runoff even when one candidate receives more than 50 percent of the vote. We propose a new measure of derservingness, called the Next-Two rule, which compares the performance of candidates to the two that immediately follow them. It identifies as contenders candidates who are bunched together near the top. We apply the Next-Two rule to several empirical examples.

Suggested Citation

  • Steven J Brams & D Marc Kilgour, 2012. "Narrowing the field in elections: The Next-Two rule," Journal of Theoretical Politics, , vol. 24(4), pages 507-525, October.
    • Handle: RePEc:sae:jothpo:v:24:y:2012:i:4:p:507-525
    DOI: 10.1177/0951629811429993
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    References listed on IDEAS

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    1. Scott L. Feld & Bernard Grofman, 2007. "The Laakso-Taagepera Index in A Mean and Variance Framework," Journal of Theoretical Politics, , vol. 19(1), pages 101-106, January.
    2. I. D. Hill, 2008. "Mathematics and Democracy: Designing Better Voting and Fair‐division Procedures," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(4), pages 1032-1033, October.
    3. Friedrich Pukelsheim & Albert W. Marshall & Ingram Olkin, 2002. "A majorization comparison of apportionment methods in proportional representation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(4), pages 885-900.
    4. Laurent Bouton, 2013. "A Theory of Strategic Voting in Runoff Elections," American Economic Review, American Economic Association, vol. 103(4), pages 1248-1288, June.
    5. Brams, Steven J. & Fishburn, Peter C., 1978. "Approval Voting," American Political Science Review, Cambridge University Press, vol. 72(3), pages 831-847, September.
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    Cited by:

    1. D. Marc Kilgour, 2016. "Approval elections with a variable number of winners," Theory and Decision, Springer, vol. 81(2), pages 199-211, August.
    2. Duddy, Conal, 2014. "Electing a representative committee by approval ballot: An impossibility result," Economics Letters, Elsevier, vol. 124(1), pages 14-16.
    3. Martin Lackner & Jan Maly, 2020. "Approval-Based Shortlisting," Papers 2005.07094, arXiv.org, revised May 2022.
    4. Martin Lackner & Jan Maly, 2025. "Approval-based shortlisting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 64(1), pages 97-142, February.

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    Keywords

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    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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