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Holt and Smith: A selective survey of experiments in political science

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Holt and Smith. 2005. A selective survey of experiments in political science.

In Brief

In an effort to better understand turnout in terms of rational choice, the authors review a few recent experiments.

Experiment 1: The authors' experiments

The authors assigned participants ("voters") into two groups. In the first group, voting cost $0.50; in the second, it cost $0.25. Participants within each group were assigned to one of two types (i.e. political parties), with three participants in each type. Participants earned $1.25 if their party won and $0.00 if it did not (less the cost of voting, if applicable).

The equilibrium predictions for these conditions are rather extreme, and it involves probabilistic strategies. In group 1 ($0.50 voting), everyone should vote with probability 0.129 or 0.871 (but everybody plays the same strategy). In group 2, everybody should vote with probability 1.

Look briefly at tables 12 and 13. You will see that group 1 converges to voting with probability 0.33 (less extreme than the 0.129 prediction, but close), and group 2 converges to p=0.67 or so (again, less extreme than the p=1 prediction). The authors speculate that this attenuation could be caused by randomness in behavior ("noise"). Comment: It could also be an artifact of the extremely small sample size; using more participants tends to reduce "noise" problems.

Experiment 2: Schram and Sonnemans (1996)

These experiments are also discussed in Palfrey's (2005) review.

Schram and Sonnemans ran similar experiments, with 6 voters of each type (party), a payoff of 2.5 for having your party win, and a voting cost of 1. Like the authors' experiments (that is, like Holt and Smith's experiments), Schram and Sonnemans derived rather extreme Nash equilibria: All players should vote with either p=0.9 or p=0.1 (they all play the same strategy, as before). And like the authors' study, S&S find that the results are less extreme than these predictions.

Unlike the authors, S&S also tested a proportional representation condition. The Nash equilibrium suggests all players should vote with p=0.1, though the actual experiment suggested less extreme results.

Experiment 3: Bornstein (1992)

Bornstein ran the first experimental tests of Palfrey and Rosenthal's (1983, 1985) "participation game" solution to the voter's paradox. Like S&S, this study examines winner-take-all (W) and proportional rules (PR) separately. Under W, everyone should contribute; under PR, nobody should. Bornstein did not find such extreme results, but he did find that participation was about 30% higher in the W condition. Apparently, "this demonstrates the importance of self-interest or criticalness" in turnout.

Experiment 4: Cason and Mui (2003)

C&M's study was similar, but added uncertainty: Some participants were unsure whether they would benefit or be hurt by a decision. As expected, this uncertainty drives participation down.

Experiment 5: Gruber and Schram (2004)

G&S introduce sociological and psychological variables by testing whether interaction with neighbors, coworkers, and family can boost turnout. They pair participants ("voters") in the study. Each pair has a "sender" (who has the option of voting in either round 1 or round 2) with a "receiver" (who can vote only in round 2, but gets to observe his partner's vote first). In different versions of the experiment, these pairs were either persistent (to model the effect of close friends) or rotating. Also, in different versions these pairs were either allies (i.e. same type) or enemies.

When the pair are allies, the sender usually chooses to vote in round 1 to send a signal, and the receiver usually heeds this signal. When the pair are enemies, the sender usually waits to vote until round 2 so as not to send any information to the receiver.

The important finding: This "neighborhood information exchange" can increase turnout by almost 50%; effects are strongest when partners are allies. This suggests that we don't just vote to change the outcome; there might also be sociological factors.