Download this Paper Open PDF in Browser

The Paradox of Grading Systems

37 Pages Posted: 28 Mar 2015  

Steven J. Brams

New York University (NYU) - Wilf Family Department of Politics

Richard Potthoff

Duke University - Department of Political Science

Date Written: March 1, 2015

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 systems, grading systems, approval voting, Condorcet paradox

JEL Classification: C61, C70, D71, D78

Suggested Citation

Brams, Steven J. and Potthoff, Richard, The Paradox of Grading Systems (March 1, 2015). Available at SSRN: https://ssrn.com/abstract=2585763 or http://dx.doi.org/10.2139/ssrn.2585763

Steven J. Brams (Contact Author)

New York University (NYU) - Wilf Family Department of Politics ( email )

Dept. of Politics
19 West 4th St., 2nd Fl.
New York, NY 10012
United States
212-998-8510 (Phone)
212-995-4184 (Fax)

HOME PAGE: http://politics.as.nyu.edu/object/stevenbrams.html

Richard Potthoff

Duke University - Department of Political Science ( email )

140 Science Drive (Gross Hall), 2nd floor
Duke University Mailcode: 90204
Durham, NC 27708-0204
United States

Paper statistics

Downloads
27
Abstract Views
203