The paper studies a simple voting system that has the potential to increase the power of minorities without sacrificing aggregate efficiency. Storable votes grant each voter a stock of votes to spend as desired over a series of binary decisions. By accumulating votes on issues that it deems most important, the minority can win occasionally. But because the majority typically can outvote it, the minority wins only if its strength of preference is high and the majority's strength of preference is low. The result is that with storable votes, aggregate efficiency either falls little or in fact rises. The theoretical predictions of our model are confirmed by a series of experiments: the frequency of minority victories, the relative payoff of the minority versus the majority, and the aggregate payoffs all match the theory.

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.

Motivated by the need for more flexible decision-making mechanisms in the European Union, the paper proposes a simple but novel voting scheme for binary decisions taken by committees that meet regularly over time. At each meeting, committee members are allowed to store their vote for future use; the decision is then taken according to the majority of votes cast. The possibility of shifting votes intertemporally allows agents to concentrate their votes when preferences are more intense, and although the scheme will not in general achieve full efficiency, making votes storable typically leads to ex ante welfare gains. The analysis in the paper suggests that the result will hold if one of the following conditions is satisfied: (i) the number of voters is above a minimum threshold; (ii) preferences are not too polarized; (iii) the horizon is long enough.

With the passage of the Voting Rights Act in 1965, the right of minorities to register and vote was largely secured. It was soon discovered, however, that minority voting did not guarantee the election of minorities or minority-preferred candidates. Indeed, efforts by states and localities in the second half of the 1960s were aimed at denying any substantial minority representation to go along with the ability to cast ballots. Eventually congressional amendments to the Act along with the Supreme Court opinion in Thornburg v. Gingles (1986) have led to efforts to eliminate electoral laws that have the effect of diluting the minority vote, whether or not they were enacted with discriminatory intent. Controversy still surrounds the matter of minority representation, however, because of the ambiguity of certain aspects of the law and because of problems in applying it to the largely single-member district context of the 1990s. This book is the most up-to-date treatment of voting rights law and the numerous controversies surrounding minority representation. The authors have extensive, firsthand experience in both the legal battles and the scholarly examination of these issues. Based on this wealth of experience, they describe the development of the law after 1965, discuss in detail the prevailing Supreme Court interpretation of the Voting Rights Act, and examine discrepancies in federal court interpretations of subsequent actions. They also introduce the reader to technical procedures for establishing standards of representation and measuring discrimination. In the final two chapters, they consider the application of voting rights law to districting in the 1990s along with the implications of recent developments for the future of representation in America.

Storable Votes and Quadratic Voting are voting systems designed to account for voters' intensity of preferences. We test their performance in two samples of California residents using data on four initiatives prepared for the 2016 California ballot. We bootstrap the original samples and generate two sets of 10,000 multi-elections simulations. As per design, both systems induce minority victories and result in higher expected welfare relative to majority voting. In our parametrization, quadratic voting induces more minority victories and achieves higher average welfare, but causes more frequent inefficient minority victories. The results are robust to different plausible rules-of-thumb in casting votes.