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Should voters be required to rank candidates in an election?

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Abstract

We compare the Condorcet Efficiencies of the plurality rule, the negative plurality rule, and the Borda rule to address the question of what might be gained by using a voting rule that requires candidate rankings. Unlike previous analyses, we consider only those voting situations for which the three rules determine different candidates as winners, because these are the cases where the Condorcet Efficiencies might actually differ across the three rules. After assessing the theoretical as well as the empirical Condorcet Efficiencies, we find that, despite considerable differences between the properties of the theoretical framework and the characteristics of three sets of empirical ranking data, all four analyses suggest that there is a considerable benefit in asking voters to submit candidate rankings.

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Notes

  1. We do not consider voting rules like approval voting or evaluative voting that do not require rankings. Accommodating rules like these requires a more general framework than the one that we use here.

  2. The notation \(n =\) 5(6)... stands for “\(n =\) 5, 11, 17...” That is, the first number indicates the smallest n for which the equation holds while the number in parentheses indicates the step size.

  3. Because every \(\textit{WSR}(\lambda )\) for \(0\le \lambda \le 1\) elects the same candidate as PR and NPR if those two rules agree on a strict winner, it is intuitive to focus on voting situations that share this property. While one could also single out voting situations for which either BR and PR or BR and NPR elect the same strict winner, doing so could have some disadvantages. For example, by subsequently discarding those voting situations, one might ignore voting situations in which the respective third voting rule is the only one that elects the CW.

  4. The notation “\(k = 0(3)33\)” stands for “all values of k, starting at 0 and ending at 33, in steps of 3.”

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Authors and Affiliations

  1. Department of Business Administration, University of Delaware, Newark, DE, 19716, USA

    William V. Gehrlein

  2. Department of Economics, University of La Réunion, Saint-Denis Cedex, La Réunion, France

    Dominique Lepelley

  3. Department of Economics, Binghamton University, Binghamton, NY, 13902, USA

    Florenz Plassmann

Authors
  1. William V. Gehrlein
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  2. Dominique Lepelley
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  3. Florenz Plassmann
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Corresponding author

Correspondence to Florenz Plassmann.

Additional information

We thank two anonymous reviewers who read our paper with unusual care and provided very helpful comments and suggestions.

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Gehrlein, W.V., Lepelley, D. & Plassmann, F. Should voters be required to rank candidates in an election?. Soc Choice Welf 46, 707–747 (2016). https://doi.org/10.1007/s00355-015-0920-5

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