FORUM

An experiment in approval voting

Editor’s note: The following article appeared in the February 1985 issue of OR/MS Today as a “Letter from the President.” At the time, John D.C. Little was president of The Institute of Management Sciences (TIMS), which later merged with the Operations Research Society of America (ORSA) to create INFORMS.

A management scientist and fellow TIMS member, Peter Fishburn, has studied the election process and proposed a simple election reform. He calls it “approval voting.” TIMS is planning to test the idea in its upcoming annual election. 

Approval voting is intended to reduce the chance that two popular candidates will split a majority group of voters and lose to a candidate of a tight-knit minority. This can typically happen in a three-way race. For example, in the l980 Senate race in New York, two liberals, Jacob Javits and Elizabeth Holtzman, ran against a conservative, Alphonse D’Amato. D’Amato won the election with 45 percent of the vote to Holtzman’s 44 percent and Javits’11 percent. Polls at the time indicated that in a two-way race Holtzman would most likely have won easily over D’Amato. In an important sense, therefore, the majority will was thwarted by the structure of the voting process. 

Fishburn and his co-worker, Steven J. Brams, propose a simple voting procedure that would overcome much of the difficulty. In approval voting the voter is permitted to vote for (approve of) as many candidates as he or she wishes. The candidate with the most votes wins. Although a voter would be permitted to vote for everybody, this would have the same effect as not voting. In the New York contest, a liberal could have voted for both Holtzman and Javits instead of being forced to choose between them. Fishburn and Brams have re-analyzed this election on the basis of polling information and show that had their system been used, Holtzman would have won with 60 percent approval and D’Amato would have had 56 percent and Javits 49 percent. 

When there are only two candidates, approval voting gives the same answer as regular, plurality voting where voters make only one choice among all candidates. In regular voting with three or more candidates, people often feel impelled to vote strategically instead of sincerely. For example, in the l980 presidential election with Reagan, Carter and Anderson, many people who preferred Anderson did not vote for him but chose between Carter and Reagan rather than “waste” their votes. Under approval voting, they could have voted for both Anderson and their preferred choice between Reagan and Carter. Although it is not reasonable to believe that this would have made any difference in l980, in a closer election a sincere preference might produce a result more consistent with the true wishes of the electorate that could occur with plurality voting.

In true management science style, Fishburn and Brams [l983] have built and analyzed a formal model of voting in elections. They rigorously define terms, state their assumptions and deduce a number of theorems to support their assertions. Whenever possible, they test their theories on empirical data and try to reconstruct past elections to see how the outcomes might have been changed under approval voting.

When a management scientist does a careful study that might be applicable to TIMS, we should seriously consider using it. Of course, changing elections procedures is not something an organization does quickly or lightly. Accordingly, the TIMS Council has authorized a non-binding, experimental ballot to test the idea in the upcoming election. For approval voting to be meaningful there must be more than two candidates for an office. The nominating committee has therefore put up three candidates for president and five nominees for U.S council instead of the usual two and four. 

TIMS members will receive a standard ballot, which will be marked in the usual way and will decide the election. In addition, however, they will receive a non-binding approval ballot in which they are permitted to vote for as many candidates as they wish. The results of the two ballots will be analyzed and reported to the TIMS Council and membership along with a recommendation whether approval voting should become a standard procedure.

It seems fitting that TIMS should recognize the professional work of its members when it is relevant to our own operations. I look forward to the experiment. The council and I welcome your reaction and comments, both now and after you have tried the process and seen the results.

References

1. S.J. Brams and P.C. Fishbum, 1978, “Approval voting,” American Political Science Review, Vol. 72, pp. 831-847.

2. S.J. Brams and P.C. Fishbum, 1983, “Approval voting,” Birkhauser, Boston.

3. P.C. Fishbum, 1981, “An analysis of simple voting systems for electing committees,” SIAM Journal on Applied Mathematics, Vol. 41, pp. 499-502.