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Narrowing the field in elections: the next-two rule

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

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 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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 30388.

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Date of creation: Apr 2011
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Handle: RePEc:pra:mprapa:30388

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

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  1. Brams,Steven J. & Taylor,Alan D., 1996. "Fair Division," Cambridge Books, Cambridge University Press, number 9780521556446, Fall.
  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.
  3. Friedrich Pukelsheim & Albert W. Marshall & Ingram Olkin, 2002. "A majorization comparison of apportionment methods in proportional representation," Social Choice and Welfare, Springer, vol. 19(4), pages 885-900.
  4. Laurent Bouton, 2012. "A Theory of Strategic Voting in Runoff Elections," Boston University - Department of Economics - Working Papers Series WP2012-001, Boston University - Department of Economics.
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