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The Rational Voter Might Show Up to Defend Civic Virtue

Last Friday, I discussed why the simple rational voter model does not predict zero turnout, despite usually being styled to do so. To be sure, the simple model cannot explain turnout of a hundred million voters in a presidential election. That does not perforce imply the model predicts zero turnout in equilibrium.

Despite the basic model’s ability to gin up significant turnout in mass elections, it nonetheless does not reasonably get us to turnout levels we typically witness in mass elections. I’ll discuss a couple of additions we can make to the simple model to increase the numbers.

The basic model has three parameters: the benefit, B, of your candidate winning, the cost to you, c, of casting a vote, and the probability, p, your vote is pivotal. One votes when pBc ≥ 0, and does not vote when pBc < 0.

The best-known fix to the basic model takes a step away from the instrumental logic of the rational voter model. The basic model’s instrumental logic holds people derive no intrinsic value from voting, we only value our vote because of the effect we have on policy when exercising it. But we can add a “k” term to the equation, representing some intrinsic value to the vote. People might value the vote as an act of civic solidarity or a civic sacrament. Among people previously denied the vote, it could be an act of self-actualization, etc. In the nineteenth century, some western states marketed the vote in Europe as an inducement to immigration. (States need not require citizenship to confer suffrage. Upwards of one-third of the voters in some western states were non-citizens, and it was all entirely legal.)

Adding the “k” term certainly works. Behavior need not be purely instrumental. The body’s simple need for energy, for example, does not explain gourmet cooking. Still, I think we can wring out a bit more turnout from thinking about instrumental behavior before we take refuge in the non-instrumental “k.”

My preferred fix entails thinking of the vote as a means by which a voter signals his or her political and policy preferences to office holders and to other voters, even when the probability of pivotally affecting an outcome approaches zero.

Some years ago, for example, a friend explained to me he did not cast a ballot in the presidential race between George W. Bush and Al Gore. But he did turn out in the next election to vote for Bush. He did this despite there being no doubt regarding which candidate would win the state’s electoral votes. He explained he turned out only to increase Bush’s popular vote total, and he did so despite increasing it only by an infinitesimal amount.

Beyond national-level office holders, 535 legislators, one president, and nine Supreme Court justices (who follow the election results—according to Mr. Dooley), there are thousands of state office holders, and over 70,000 local governments in the U.S. Casting one’s vote signals information about one’s preferences, even if in a crude fashion, to all of these office holders and to other voters regarding the location of the median voter and aggregate political preferences more generally. And relative to other modes of providing information about one’s preferences to all of these other political actors, one’s vote is a relatively inexpensive way to signal that information.

Finally, we can think about the structure of utility functions. Rather than thinking of smooth tradeoffs between policy dimensions, many voters might act in a way, say, to mini-max their regret over election outcomes, that is, they want to minimize the maximum amount of regret they would have in their actions, including the vote. Think of Florida in Bush v. Gore, or Michigan in 2016.

My suspicion is these fixes to the simple model can account for turnout levels we observe in mass elections. And if not, we can always throw in the non-instrumental “k.”

I’ll conclude in my next post chatting about the interaction between the rational voter model and the median voter model, and why we still observe positive turnout, as well as (some) differences between the parties.

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