Professor Jack Nagel: In electoral systems debate, math is only as good as assumptions about behavior

Theres a curious paradox behind the debate over ranked-choice voting: Vocal critics of the reform such as Clay Shentrup, the Berkeley, Calif.-based co-founder of the Center for Election Science and the writer of the July 9 commentary in the News Tribune, Dont be taken in by unproven ranked-choice voting claims actually agree with its supporters about why conventional voting methods should be replaced.

Nevertheless, hentrup and his organization vehemently oppose Duluths adoption of ranked-choice voting via the forthcoming referendum, just as they tried to block it in the Twin Cities.

Why? Shentrup wants to hold out for either of two alternative reforms, score voting or approval voting. Neither ever has been used in any governmental election. Lacking tests from real politics, proponents rely on mathematical analyses they think prove those methods would be better than ranked-choice voting.  

These critics resemble a long succession of radical purists who choose to attack pragmatic reformers rather than defenders of the status quo. Their desire to hold out for allegedly superior reforms might be persuasive if score voting and approval voting would work better than ranked-choice voting, but I believe they would not.

Mathematical proofs are only as good as their premises. In evaluating electoral systems, the key assumptions are about how people will vote. In particular, will they vote sincerely so that ballots represent true feelings? Or does the voting method give a strong incentive to vote strategically so that many voters misrepresent their preferences?Score voting and approval voting are both highly vulnerable to strategic voting. A clue to this problem is given by their odd-bedfellows alliance. At first blush, they seem like systems whose supporters should disagree. Score voting invites the voter to give more information than ranked-choice voting, whereas approval voting requires the voter to give less information.

For example, with a ranked-choice ballot, a voter might rank candidate A first, B second, and C third. Score voting, in contrast, allows the voter to assign candidates any score within a specified range, such as 0 to 10. Thus a sincere voter might score A 8 (good, but not perfect), C 3 (bad, but not the devil incarnate), and B some number in between. The approval ballot allows voting for any number of candidates, but all votes count equally. Someone who likes B almost as much as A might vote for or approve of both.

The appeal of score voting is understandable. If the system works as intended, it provides a more sensitive register of voters feelings than conventionalsingle-vote ballots, ranked-choice voting or approval voting. However, that if is a big problem in the rough-and-tumble world of real politics. If a bloc of voters really wants A to win, his chances will be greatest if they all give him the maximum 10, even if they really think he deserves only 8. Similarly, if they are determined to defeat C, her score should be lowered from a sincere 3 to a strategic 0. As for B, if hes almost as good as A and the real goal is to keep C out of power, then the best strategy may be to give B a 10; but if B is nearly as bad as C and the overriding objective is to elect A, then B should be downgraded to 0.

If all scores are spread in this fashion to 10 or 0, then score voting becomes equivalent to approval voting. That is why there is an alliance between advocates of the two methods. Approval voting is the fallback for score voting.

But is approval voting itself reliable? During the 1980s, I promoted experiments with approval voting, including a presidential straw vote by Pennsylvania Democrats and adoption by a large nongovernmental association (which has since abandoned it). In some cases, approval voting worked as intended by preventing the splitting of a majority between two similar candidates. Unfortunately, in other contests, blocs of voters strategically bullet-voted for only one candidate, even though there were good reasons to believe they sincerely approved of more than one.

In short, under the pressure of real competition, score voting may degenerate into approval voting, and approval voting in turn can collapse into the single-vote system all these reforms are intended to replace.

Is ranked-choice voting immune from strategic voting? One contribution of mathematics to our understanding of elections is a proof that all reasonable systems of voting must be vulnerable to misrepresentation of preferences under some circumstances. The real questions are: How frequently do those occasions occur? How obvious is the temptation to vote strategically? How easy is it to do? And how serious are the consequences?

On all these counts, I believe ranked-choice voting is more resistant to strategic manipulation than either score or approval voting.

Adding in its other advantages over conventional systems in Duluth and elsewhere economy, turnout, ability to express more choices and ensuring winners who are not opposed by a majority a vote in favor of this tested reform seems to me a wise decision. 

Jack Nagel of Swarthmore, Pa., is a professor emeritus of political science at the University of Pennsylvania who investigated alternatives to the single-winner plurality elections that dominate in the U.S. and has done extensive research and written numerous articles on this subject. He wrote this for the News Tribune.





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