Of Ballots and Battles–Voting’s Coordination Problem

Who would you sincerely like to see as the next president? Did you approve of Obama’s support of gay marriage, but chafe at his bailout of the auto industry? Are you keen on Romney’s plans to cut taxes but worried about his stance on women’s healthcare? Maybe you’d like to pick someone else entirely? Voting presents a classic coordination problem. If you follow your purest impulse and write in the name of the person you think is going to run the country as you would like, as opposed to someone you could merely ‘accept’ as president (but who stands a realistic chance of attracting other votes), you fail to act strategically. Strategy, of course, requires cooperation. But how do the interactions between one another and the institutional structures we have created make cooperation possible? Lee Cronk and Beth Leech are the authors of Meeting at Grand Central: Understanding the Social and Evolutionary Roots of Cooperation, a study of how every facet of our lives is impacted by cooperative interactions. Read their post here on how the electoral process has evolved to address the seemingly simple but very complex problem that arises when the preferences and desires of individuals  overlap, but not quite.


Of Ballots and Battles

Lee Cronk and Beth L. Leech


The upcoming major party conventions and the primaries that preceded them are all about one thing: Whose names will appear on the ballot in November. But why do we need a ballot at all? After all, ballots constrain our choices. People are often angry and may even decide not to vote when their preferred candidate fails to appear on the ballot. Why, then, don’t we simply write down the names of the people that we would prefer in a particular office? Wouldn’t that be the purest expression of voters’ desires?

Of course, if everyone walked into the voting booth with nothing but a pen and a blank piece of paper, they would have 150 million people to chose from (that’s about how many currently meet the requirements set out in the Constitution as native-born Americans 35 or older who have lived in the United States for at least fourteen years.) Some people would indeed vote for their heart’s true desire – the one person out of all who are eligible for a particular office that they would most like to see in that position. But some savvy voters would realize that even though they think their Uncle Ned would make a great president, so few others are likely to agree – or even to know who Ned is – that those voters would instead vote for someone they could accept as president but who also has a chance of attracting enough other votes to actually get elected. In technical terms, those voters would vote “strategically” rather than in accordance with their “sincere preferences.” If any one candidate could convince a plurality of the electorate to vote for him or her strategically, even if no voters at all preferred him or her over all other possibilities, then he or she would win the election.

The voter’s dilemma in such circumstances poses a coordination problem. Coordination problems occur when people have identical or at least overlapping preferences regarding some outcome, but they lack the common knowledge necessary to achieve those preferences. Solutions to the coordination problems usually come from shared knowledge. One very simple coordination problem is addressed in the title of our forthcoming  book, Meeting at Grand Central: Understanding the Social and Evolutionary Roots of Cooperation. About fifty years ago, Yale economist Thomas Schelling (now at the University of Maryland) asked people in New Haven, Connecticut a simple question: If you were in New York City and you knew that you were to meet a friend there, but you and your friend had not previously agreed upon a time and place, where would you go, and when would you go there? Schelling’s respondents mostly said Grand Central Terminal at noon. Because commuter trains from New Haven arrive at Grand Central, it served as a prominent, salient solution to the coordination problem for Schelling’s respondents.

As UCLA political scientist Michael Chwe has pointed out in his book Rational Ritual: Culture, Coordination, and Common Knowledge (Princeton University Press, 2003), solving coordination problems requires not only common knowledge about how they can be solved, but also common knowledge that there is common knowledge – in Chwe’s terminology, “common metaknowledge.” Imagine, for example, the coordination problem facing people in a crowded theater when a fire alarm goes off. Even if everyone in the theater knows that the best course of action is for everyone to move in an orderly fashion toward the exits, if they do not also know that everyone else also knows that this is the best way to behave, then they have no reason to act on their knowledge. The result of a lack of common metaknowledge is thus the same as a lack of common knowledge: a lack of coordination and a rush toward the exits.

From the voter’s point of view, elections present a coordination problem. Everyone has his or her own preferences regarding who holds elected office. Those preferences do not overlap perfectly, and for some people they may overlap not at all, but they do overlap enough that coordination is possible, at least in principle. This sort of coordination problem with a large dollop of conflict is similar to a famous game theoretical scenario called The Battle of the Sexes. Imagine a husband and a wife faced with the decision of whether to spend the evening at a boxing match or opera. The husband prefers the boxing match and the wife the opera, but both prefer spending the evening together rather than apart. Thus, their preferences overlap, but only partly. Similarly, you and your neighbor might prefer different candidates in your heart of hearts, but you have enough in common that you can agree that some third candidate is acceptable and perhaps also that some fourth candidate is not. In that case, you and your neighbor might set aside your hearts’ desires and instead vote for the candidate that you both find acceptable, instead.

However, doing this requires that you know that your neighbor is also likely to vote strategically, and vice versa: common knowledge and common metaknowledge. Ballots – and the primaries and conventions that create them – help solve this coordination problem. By reducing the range of choices down to just those few individuals who actually have a chance of winning, ballots help voters coordinate their efforts. Although very few will end up with the outcome that they most prefer, a plurality of people will end up with an outcome that they can accept. In the 1950s, this logic was developed by French sociologist Maurice Duverger and is now enshrined in what is commonly known as “Duverger’s Law”: in a place with single member district plurality voting, the efforts of voters to avoid wasting their votes will lead, in most instances, to a ballot with just two viable candidates. Stanford political scientist Gary Cox has since generalized Duverger’s Law to multi-member districts, showing that the tendency in a district with M members will be for the ballot to converge on M + 1 candidates.

We hope that we have convinced you of the value of ballots as solutions to coordination problems. However, if you still chafe at the way that they constrain your electoral choices, take heart: People who live in constituencies in which the outcome of an election is not in doubt can feel free to vote as their consciences dictate, whether that means voting for a candidate from the two major parties, voting for a third party candidate, or writing in someone’s name. In that situation, following one’s heart is not risky – and strategic voting is not tempting – because the winner is already known. Does it then follow that those of us who live in “battleground” states where the outcome is uncertain should set aside good old Uncle Ned and focus instead on those few individuals whose names actually do appear on the ballot? Perhaps! This is a question we will revisit in our next post on this blog, in which we will explore some of the reasons why people vote in the first place.


Lee Cronk is professor of anthropology at Rutgers University. He is the author of That Complex Whole: Culture and the Evolution of Human Behavior. Beth L. Leech is associate professor of political science at Rutgers University. She is the coauthor of Basic Interests: The Importance of Groups in Politics and in Political Science (Princeton).