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Narrowing the field in elections: the next-two rule


  • Brams, Steven J.
  • Kilgour, D. Marc


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 depend on the distribution of votes among 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 deservingness, called the Next-Two rule, which compares the performance of candidates to the two that immediately follow them. It never prescribes a runoff when one candidate receives more than 50 percent of the vote. More generally, it identifies as contenders candidates who are bunched together near the top and, unlike the Jefferson and Webster methods, never declares that all candidates are contenders. We apply the Next-Two rule to several empirical examples, including one (elections to major league baseball’s Hall of Fame) in which more than one candidate can be elected.

Suggested Citation

  • Brams, Steven J. & Kilgour, D. Marc, 2011. "Narrowing the field in elections: the next-two rule," MPRA Paper 30388, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:30388

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    References listed on IDEAS

    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. Laurent Bouton, 2013. "A Theory of Strategic Voting in Runoff Elections," American Economic Review, American Economic Association, vol. 103(4), pages 1248-1288, June.
    3. 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.
    4. 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.
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    Cited by:

    1. Duddy, Conal, 2014. "Electing a representative committee by approval ballot: An impossibility result," Economics Letters, Elsevier, vol. 124(1), pages 14-16.
    2. D. Marc Kilgour, 2016. "Approval elections with a variable number of winners," Theory and Decision, Springer, vol. 81(2), pages 199-211, August.

    More about this item


    voting; contenders in elections; runoffs; apportionment; fairness;

    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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