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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, 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.



Item Type: MPRA Paper -

Original Title: The Paradox of Grading Systems-

Language: English-

Keywords: Voting; elections; ranking system; grading system; approval voting; Condorcet paradox-

Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic AnalysisC - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C70 - GeneralD - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice ; Clubs ; Committees ; AssociationsD - Microeconomics > D7 - Analysis of Collective Decision-Making > D78 - Positive Analysis of Policy Formulation and Implementation-





Author: Brams, Steven

Source: https://mpra.ub.uni-muenchen.de/63268/



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