A mathematical proof of Duverger's Law

[No abstract

Protecting Minorities in Large Binary Elections. A Test of Storable Votes Using Field Data

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.Storable Votes, Referendums, Minorities, Majority Voting, Experiments

A mathematical proof of Duverger's Law

[No abstract

Protecting Minorities in Binary Elections

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

Protecting Minorities in Binary Elections: A Test of Storable Votes Using Field Data

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.

Government By and For Millenial America: A Blueprint for 21st Century Government

Using this generation's unique ethos and commitment to pragmatic problem-solving, Millennials across the country have collaborated to design their vision for a 21st century democracy and reject the idea that our system is too broken, too stagnant, and too outdated. They have identified the parts of the system that need to be fixed while articulating what a true democracy should look like. Government By and For Millennial America, the third installment of our blueprint series, tackles some of the most fundamental, divisive, and difficult questions on the purpose of government in furthering our country's progress: how can we hear from more voices? How can we be more transparent? How can government be more egalitarian? How can we both support individual communities and the common good of every American? Most importantly, this pursuit is grounded in one fundamental idea that defines America's distinctive pursuit of self-governance: in the words of our namesake, Let us never forget that government is ourselves and not an alien power over us. The ultimate rulers of our democracy are not a President and senators and congressmen and government officials, but the voters of this country. - President Franklin D. Roosevelt We set out to craft a blueprint, and discovered, in conversations with over a thousand young people across the country, that the Millennial generation is not yet ready to give up on America's ever evolving experiment in a government by and for the people

The metric distortion of multiwinner voting

We extend the recently introduced framework of metric distortion to multiwinner voting. In this framework, n agents and m alternatives are located in an underlying metric space. The exact distances between agents and alternatives are unknown. Instead, each agent provides a ranking of the alternatives, ordered from the closest to the farthest. Typically, the goal is to select a single alternative that approximately minimizes the total distance from the agents, and the worst-case approximation ratio is termed distortion. In the case of multiwinner voting, the goal is to select a committee of k alternatives that (approximately) minimizes the total cost to all agents. We consider the scenario where the cost of an agent for a committee is her distance from the q-th closest alternative in the committee. We reveal a surprising trichotomy on the distortion of multiwinner voting rules in terms of k and q: The distortion is unbounded when q≤k/3, asymptotically linear in the number of agents when k/3k/