Brams, Steven and Potthoff, Richard (2015): The Paradox of Grading Systems.
Preview |
PDF
MPRA_paper_63268.pdf Download (480kB) | Preview |
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 Analysis C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C70 - General D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice ; Clubs ; Committees ; Associations D - Microeconomics > D7 - Analysis of Collective Decision-Making > D78 - Positive Analysis of Policy Formulation and Implementation |
Item ID: | 63268 |
Depositing User: | Steven J. Brams |
Date Deposited: | 28 Mar 2015 15:52 |
Last Modified: | 07 Oct 2019 17:19 |
References: | Alcantud, José Carlos R., and Annick Laruelle (2014). “Dis&Approval Voting: A Characterization.” Social Choice and Welfare 43, no. 1: 1-10. Arrow, Kenneth J. (1951; rev. ed., 1963). Social Choice and Individual Values. New Haven, CT: Yale University Press. Balinski, Michel L., and Rida Laraki (2011). Majority Judgment. Cambridge, MA: MIT Press. Baujard, Antoinette, Frédéric Gavrel, Herrade Igersheim, Jean-François Laslier, and Isabelle Lebon (2014). “Who’s Favored by Evaluative Voting? An Experiment Conducted during the 2012 French Presidential Election.” Preprint. http://dx.doi.org/10.2139/ssrn.2554474 Bowler, Shaun, Todd Donovan, and David Brockington (2003). Electoral Reform and Minority Representation: Local Experiments with Alternative Elections. Columbus, OH: Ohio State University Press. Brams, Steven J. (1975; rev. ed., 2003). Game Theory and Politics. Mineola, NY: Dover. Brams, Steven J. (2008). Mathematics and Democracy: Designing Better Voting and Fair-Division Procedures. Princeton, NJ: Princeton University Press. Brams, Steven J., and Peter C. Fishburn (1978). “Approval Voting.” American Political Science Review 72, no. 3 (September): 831-847. Brams, Steven J., and Peter C. Fishburn (1983; rev. ed., 2007). Approval Voting. New York: Springer. Brams, Steven J., and Peter C. Fishburn (2005). “Going from Theory to Practice: The Mixed Success of Approval Voting.” Social Choice and Welfare 25, no. 2: 457-474. Brams, Steven J., Peter C. Fishburn, and Samuel Merrill III (1988). “The Responsiveness of Approval Voting: Comments on Saari and Van Newenhizen” and “Rejoinder to Saari and Van Newenhizen.” Public Choice 59, no. 2 (November): 121-131, 149. Brams, Steven J., and M. Remzi Sanver, “Voting Systems That Combine Approval and Preference,” in Steven J. Brams, William V. Gehrlein, and Fred S. Roberts (eds.) (2009). The Mathematics of Preference, Choice, and Order: Essays in Honor of Peter C. Fishburn. Springer, pp. 215-237. Camps, Rosa, Xavier Mora, and Laia Saumell (2014). “Choosing by Means of Approval-Preferential Voting: The Revised Approval Choice.” Preprint. http://mat.uab.cat/departament/Publ/prep/p21_14.pdf Center for Election Science (2015). http://www.electology.org Center for Range Voting (2015). http://rangevoting.org Laslier, Jean-François, and M. Remzi Sanver (eds.). Handbook on Approval Voting. Berlin: Springer. Felsenthal, Dan S. (1989). “On Combining Approval with Disapproval Voting.” Behavioral Science 34 (1989): 53-60. Felsenthal, Dan S., and Moshé Machover (eds.) (2012). Electoral Systems: Paradoxes, Assumptions, and Procedures. Berlin: Springer. Hillinger, Claude (2005). “The Case for Utilitarian Voting.” Homo Oeconomicus 22, no. 3: 295-321. Merrill, Samuel III, and Jack Nagel (1987). “The Effect of Approval Balloting on Strategic Voting under Alternative Decision Rules,” American Political Science Review 81, no. 2 (June): 509-524. Potthoff, Richard F. (2013). “Simple Manipulation-Resistant Voting Systems Designed to Elect Condorcet Candidates and Suitable for Large-Scale Public Elections.” Social Choice and Welfare 40, no. 1: 101-122. Potthoff, Richard F. (2014). “Condorcet Completion Methods That Inhibit Manipulation through Exploiting Knowledge of Electorate Preferences.” Games 5, no. 4: 204-233. Regenwetter, Michel, Bernard Grofman, A. A. J. Marley, and Ilia Tsetlin (2006). Behavioral Social Choice: Probabilistic Models, Statistical Inference, and Applications. Cambridge, UK: Cambridge University Press. Saari, Donald G., and Jill Van Newenhizen (1988). “Is Approval Voting an ‘Unmitigated Evil’: A Response to Brams, Fishburn, and Merrill.” Public Choice 59, no. 2 (November): 133-147. Sanver, M. Remzi (2010). “Approval as an Intrinsic Part of Preference,” in Jean-François Laslier and M. Remzi Sanver (eds.), Handbook on Approval Voting. Berlin: Springer, pp. 469-481. |
URI: | https://mpra.ub.uni-muenchen.de/id/eprint/63268 |