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Democratic systems are built, with good reason, on majoritarian principles, but their legitimacy requires the protection of strongly held minority preferences. The challenge is to do so while treating every voter equally and preserving aggregate welfare. One possible solution is storable votes: granting each voter a budget of votes to cast as desired over multiple decisions. During the 2006 student elections at Columbia University, we tested a simple version of this idea: voters were asked to rank the importance of the different contests and to choose where to cast a single extra "bonus vote," had one been available. We used these responses to construct distributions of intensities and electoral outcomes, both without and with the bonus vote. Bootstrapping techniques provided estimates of the probable impact of the bonus vote. The bonus vote performs well: when minority preferences are particularly intense, the minority wins at least one of the contests with 15--30 percent probability; and, when the minority wins, aggregate welfare increases with 85--95 percent probability. When majority and minority preferences are equally intense, the effect of the bonus vote is smaller and more variable but on balance still positive.

Democratic systems are built, with good reason, on majoritarian principles, but their legitimacy requires the protection of strongly held minority preferences. The challenge is to do so while treating every voter equally and preserving aggregate welfare. One possible solution is storable votes: granting each voter a budget of votes to cast as desired over multiple decisions. During the 2006 student elections at Columbia University, we tested a simple version of this idea: voters were asked to rank the importance of the different contests and to choose where to cast a single extra "bonus vote," had one been available. We used these responses to construct distributions of intensities and electoral outcomes, both without and with the bonus vote. Bootstrapping techniques provided estimates of the probable impact of the bonus vote. The bonus vote performs well: when minority preferences are particularly intense, the minority wins at least one of the contests with 15--30 percent probability; and, when the minority wins, aggregate welfare increases with 85--95 percent probability. When majority and minority preferences are equally intense, the effect of the bonus vote is smaller and more variable but on balance still positive.

Democratic systems are built, with good reason, on majoritarian principles, but their legitimacy requires the protection of strongly held minority preferences. The challenge is to do so while treating every voter equally and preserving aggregate welfare. One possible solution is storable votes: granting each voter a budget of votes to cast as desired over multiple decisions. During the 2006 student elections at Columbia University, we tested a simple version of this idea: voters were asked to rank the importance of the different contests and to choose where to cast a single extra "bonus vote," had one been available. We used these responses to construct distributions of intensities and electoral outcomes, both without and with the bonus vote. Bootstrapping techniques provided estimates of the probable impact of the bonus vote. The bonus vote performs well: when minority preferences are particularly intense, the minority wins at least one of the contests with 15.30 percent probability; and, when the minority wins, aggregate welfare increases with 85.95 percent probability. When majority and minority preferences are equally intense, the effect of the bonus vote is smaller and more variable but on balance still positive.

The legitimacy of democratic systems requires the protection of minority preferences while ideally treating every voter equally. During the 2006 student elections at Columbia University, we asked voters to rank the importance of different contests and to choose where to cast a single extra "bonus vote," had one been available — a simple version of Storable Votes. We then constructed distributions of intensities and electoral outcomes and estimated the probable impact of the bonus vote through bootstrapping techniques. The bonus vote performs well: when minority preferences are particularly intense, the minority wins at least one contest with 15-30 percent probability; when the minority wins, aggregate welfare increases with 85-95 percent probability. The paper makes two contributions: it tests the performance of storable votes in a setting where preferences were not controlled, and it suggests the use of bootstrapping techniques when appropriate replications of the data cannot be obtained.

Democratic systems are built, with good reason, on majoritarian principles, but their legitimacy requires the protection of strongly held minority preferences. The challenge is to do so while treating every voter equally and preserving aggregate welfare. One possible solution is storable votes: granting each voter a budget of votes to cast as desired over multiple decisions. During the 2006 student elections at Columbia University, we tested a simple version of this idea: voters were asked to rank the importance of the different contests and to choose where to cast a single extra "bonus vote," had one been available. We used these responses to construct distributions of intensities and electoral outcomes, both without and with the bonus vote. Bootstrapping techniques provided estimates of the probable impact of the bonus vote. The bonus vote performs well: when minority preferences are particularly intense, the minority wins at least one of the contests with 15-30 percent probability; and, when the minority wins, aggregate welfare increases with 85-95 percent probability. When majority and minority preferences are equally intense, the effect of the bonus vote is smaller and more variable but on balance still positive.