Voting Correctly in Lab Elections with Monetary Incentives: The Impact of District Magnitude

By André Blais (University of Montreal)

What is the story?

In a recent article, we examined how electoral rules influence correct voting in lab elections. We defined a correct vote as a vote that maximizes a subject’s payoff. We found that correct voting is more frequent under plurality than under proportional representation (PR).

The lab experiment

We organized twelve experimental sessions, six in Brussels and six in Montreal. In each of them, 21 subjects were invited to play the role of voters in a series of 24 consecutive elections. For each election, they had to decide to vote for one out of four parties. We varied our main treatment variable, i.e. the district magnitude (DM) from single-member plurality (DM=1) to a pure proportional system (DM=21), from sessions to sessions.

At the beginning of each session, we randomly assigned a “voter profile” to each subject (this voter profile was randomly reshuffled every three elections, just as the number of subjects with a given profile). This profile determined the voter’s preferences regarding the four parties. The general idea was that each subject strongly preferred one party and strongly disliked another one, and the two others in between. The payoff structure depended on two features: the proportion of seats each party won and the voter profile. The payoff of each subject increased with the number of seats obtained by the parties that she liked. Finally, before each election, subjects were informed about the distribution of profiles among them and where subsequently asked to indicate how many votes they thought each party would obtain.

The findings

All in all, 73% of the votes cast in the various elections were “objectively” correct, that is, the decision made by the participant maximized her payoff, given the actual votes cast by the other participants. The percentage is almost the same (74 %) with the subjective approach, when we use the participants’ anticipation about the results rather than the actual votes.

We found that the participants voted more correctly (whether defined objectively or subjectively) in single-member plurality elections than in multiple-member PR elections. But we found little difference whether DM was 3, 5, 7, 9 or 21, and so the contrast is between plurality and PR.


In a recent article, we showed that correct voting, as defined there, is more frequent under the plurality rule than under PR. The reason is simple: it is easier for voters to figure out whether they should vote sincerely for their preferred party or strategically support another one when the only way to win a seat is to have more votes than all the competitors. The plurality rule has many perverse consequences but people easily understand the logics. Things are not so easy with PR.

For more information, see André Blais, Jean-Benoit Pilet, Simon Labbé-St-Vincent, and Rafael Treibich. Forthcoming. Voting Correctly in Lab Elections with Monetary Incentives: The Impact of District Magnitude. Party Politics.

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