Grading Candidates » American Scientist

October 24, 2016

Grading Candidates, w. medians is robust but affected by the no-show paradox – extra votes for top-ranked can hurt


Although the median is generally less manipulable than the mean, which would seem to favor majority judgment over range voting, majority judgment suffers from a bizarre problem that range voting and approval voting do not—its vulnerability to the “no-show paradox,” as illustrated by the following example, in which five voters give candidates A and B the following grades:

Notice that all three voting systems, including approval voting, render A the winner, and that A receives a higher grade than B from every voter except the second one.

Now suppose that two new voters show up, and each gives a grade of Excellentto candidate A and a grade of Very Good to candidate B. These additions would not change the outcome under range and approval voting; in fact, they would give a bigger victory to A. By contrast, under majority judgment, the new median would be Very Good for B but would remain Good for A, so B would win, even though it was A who received more support from the new voters.

Although the new voters have given higher grades to A than to B, their votes have backfired, electing B instead, so they would have been better off not showing up. This paradox is clearly antithetical to democratic choice—more support should help, not hurt. The authors acknowledge that majority judgment is vulnerable to the no-show paradox, but they dismiss this as “of little real importance” in practice.

Majority judgment is not the only system in which additional support can sometimes hurt a candidate. In some systems—such as the Hare system of single transferable vote (also known as the alternative vote or instant-runoff voting), which is used in Australia, among other places—voters rank all of the candidates. Those who receive the fewest first-choice votes are sequentially eliminated, and the votes cast for them are transferred to the next-lower choice who remains until one candidate receives a majority. Under this system, a voter who raises a candidate in his or her ranking can actually cause that candidate to lose. Voting systems that allow this to occur are said to be nonmonotonic.


Grading Candidates

Steven J. Brams

MAJORITY JUDGMENT: Measuring, Ranking, and Electing. Michel Balinski and Rida Laraki. xvi + 414 pp. The MIT Press, 2010. $40.