To vote or to abstain? An experimental test of rational calculus in FPTP and PR elections

By André Blais, University of Montreal

What is the story?

Many economists and political scientists explain the decision to vote or to abstain using a rational choice model. In a recent article, we tested the rational choice model of voting in the lab. We performed numerous experiments in Brussels, Montreal, and Paris, in which participants had to decide whether to vote or not in a number of first past the post (FPTP) and proportional representation (PR) elections. The overwhelming thrust of the evidence we found is inconsistent with the rational choice model, both in FPTP and PR elections, both at the aggregate and individual levels, and in both static and dynamic terms.


In each experimental session, we organized two series of ten elections with a group 21 participants. For each election, there were two parties (named A and B) located respectively at 5 and 15 on a 0 to 20 scale. Each participant was randomly allocated a different position on the scale (random draw with no replacement). One participant was thus located at each of the 21 positions.

At each election, participants voted for party A, for party B, or abstained. A participant’s gain equalled 16 points minus the distance between the winning position and the participant’s position. Voting cost 1 point. How votes translate into winning positions depended on the voting rule. There were two series of ten elections, one series under FPTP and one under PR. Under FPTP, the winning position is that of the party with the most votes (there is a random draw in case of a tie). Under PR, the winning position depends on the relative support given to the two parties. The winning position was a weighted average of the candidates’ positions (5 and 15), where the weight given to a candidate’s position is the vote share obtained by that candidate. For example, if 70% of the votes go to A, the winning position was 8.


In the article, we tested the predictions of rational choice theory from three different angles. First, we compared aggregate turnout with the Nash equilibrium predictions. Figure 1 reports the evolution of the proportion of participants voting by elections under both FPTP and PR. In both instances, we observed a slight decrease of this proportion throughout elections. However, were not able to draw any relation with the Nash equilibrium predictions (according to theory, turnout should be higher under FPTP than under PR.

Figure 1: Evolution of aggregate turnout.

Second, we compare individual decisions with those derived from a rational calculus and count the number of decisions that were consistent with the rational recommendation. We found that in most cases participants made the wrong choice, that is, they voted even if their expected payoff was negative or they abstained when the payoff was positive.

Finally, we determined, still at the individual level, whether, at the margin, participants were more likely to vote as the expected payoff increased. The hypothesis was partially confirmed in FPTP elections. On the one hand, the participants were indeed more likely to vote when the stakes were higher, which is in line with the predictions of rational choice. On the other hand, contrary to the theory, the participants were not more prone to vote if their decision was pivotal. Moreover, the theory performed very poorly in PR elections because the participants were more inclined to vote when turnout in their group was high and when the party they supported was strong, which is exactly the opposite of what the theory would recommend.


We concluded that the rational choice model is not very useful in making sense of the decision to vote or abstain during elections. Many analysts reached this conclusion in the past. However, previous research was based almost entirely based on survey data. The evidence presented here indicates that the verdict is the same when we move to the lab.

The fact that the rational choice model is not supported in the lab is quite telling. If it the model is of little help to understand people’s behaviour there, it is probably even worse in real-life elections. There are indeed various factors biasing the tests in favour of the rational model in the lab. Most of the participants were university students. The elections that they participated in are emotion free. The participants were told after each election how many points they won and they had every incentive to think about how best to maximize their points and ultimate monetary payments. Furthermore, because of the small number of voters in the lab the probability of being pivotal was not infinitely small (as it is the case in real-life elections). Yet, people’s behaviour systematically diverges from the predictions of rational choice.

It would seem, then, that, as Barry1 claimed a long time ago, when it comes to making sense of the turnout decision we may have to learn more from sociologists than from economists.

For further details and analyses, see André Blais, Jean-Benoit Pilet, Karine Van der Straeten, Jean-François Laslier, and Maxime Héroux-Legault. 2014. To Vote or to Abstain? An Experimental Test of Rational Calculus in First Past the Post and PR Elections. Electoral Studies, 36: 39-50.

  1. B. Barry (1978). Sociologists, Economists, and Democracy. University of Chicago Press, Chicago. 

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