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The Paradox of Grading Systems

Steven Brams and Richard Potthoff

MPRA Paper from University Library of Munich, Germany

Abstract: We distinguish between (i) voting systems in which voters can rank candidates and (ii) those in which they can grade candidates, such as approval voting, in which voters can give two grades—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; elections; ranking system; grading system; approval voting; Condorcet paradox (search for similar items in EconPapers)
JEL-codes: C61 C70 D71 D78 (search for similar items in EconPapers)
Date: 2015-03-26
New Economics Papers: this item is included in nep-cdm and nep-pol
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