This paper presents a large-scale experiment on the Approval Voting rule that took place during the 2002 French presidential election. We describe the experiment and its main results. The findings are as follows: (i) Such an experiment is feasible, and very well accepted by voters. (ii) The principle of approval voting is easily understood and accepted. (iii) Within the observed political context, compared to the official first-round vote, approval voting modifies the overall ranking of candidates. (iv) The candidates Le Pen and Chirac, more than the others, were able to convert approval votes into official first-round votes.

Several probabilistic models for subset choice have been proposed in the literature, for example, to explain approval voting data. We show that Marley et al.'s latent scale model is subsumed by Falmagne and Regenwetter's size-independent model, in the sense that every choice probability distribution generated by the former can also be explained by the latter. Our proof relies on the construction of a probabilistic ranking model which we label the “repeated insertion model.” This model is a special case of Marden's orthogonal contrast model class and, in turn, includes the classical Mallows φ-model as a special case. We explore its basic properties as well as its relationship to Fligner and Verducci's multistage ranking model.

Survey experiments that investigate how voting procedures affect voting behavior and election outcomes use hypothetical questions and non-representative samples. We present here the results of a novel survey experiment that addresses both concerns. First, the winning party in our experiment receives a donation to its campaign funds inducing real consequences for voting. Second, we run an online experiment with a Dutch national representative sample (N = 1240). Our results validate previous findings using a representative sample, in particular that approval voting leads to a higher concentration in votes for smaller parties and strengthens centrist parties in comparison to plurality voting. Importantly, our results suggest that voting behavior is not affected by voting incentives and can be equally reliably elicited with hypothetical questions.

In a controlled laboratory experiment we investigate whether time pressure influences voting decisions, and in particular the degree of strategic (insincere) voting. We find that participants under time constraints are more sincere when using the widely-employed Plurality Voting method. That is, time pressure might reduce strategic voting and hence misrepresentation of preferences. However, there are no effects for Approval Voting, in line with arguments that this method provides no incentives for strategic voting.