Public Choice

, Volume 165, Issue 3, pp 193–210

The paradox of grading systems

Article

DOI: 10.1007/s11127-015-0303-6

Cite this article as:
Brams, S.J. & Potthoff, R.F. Public Choice (2015) 165: 193. doi:10.1007/s11127-015-0303-6
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Abstract

We distinguish between (i) voting systems in which voters can rank candidates and (ii) those in which they can grade candidates, using two or more grades. In approval voting, voters can assign two grades only—approve (1) or not approve (0)—to candidates. While two grades rule out a discrepancy between the average-grade winners, who receive the highest average grade, and the superior-grade winners, who receive more superior grades in pairwise comparisons (akin to Condorcet winners), more than two grades allow it. We call this discrepancy between the two kinds of winners the paradox of grading systems, which we illustrate with several examples and whose probability we estimate for sincere and strategic voters through a Monte Carlo simulation. We discuss the tradeoff between (i) allowing more than two grades, but risking the paradox, and (ii) precluding the paradox, but restricting voters to two grades.

Keywords

Voting and elections Grading systems Ranking systems Approval voting Condorcet winner Monte Carlo simulation 

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of PoliticsNew York UniversityNew YorkUSA
  2. 2.Department of Political Science and Social Science Research InstituteDuke UniversityDurhamUSA

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