Mathematics and democracy: Designing better voting and fair-division procedures

  title={Mathematics and democracy: Designing better voting and fair-division procedures},
  author={Steven J. Brams},
  journal={Math. Comput. Model.},
  • S. Brams
  • Published 1 November 2008
  • Economics
  • Math. Comput. Model.

Approval Voting in Large Electorates

The strategic analysis of voting rules has given some insight into the understanding of their properties. However, one can assert that these analyses are “too rich” in the sense that they show that a

Computational aspects of approval voting and declared-strategy voting

Computational social choice is a relatively new discipline that explores issues at the intersection of social choice theory and computer science. Designing a protocol for collective decision-making

Book Review

There is the theory of social choice and then there is the actual practice of politics. One concern of the theory of social choice is how best to aggregate the individual preferences of voters to

The excess method: a multiwinner approval voting procedure to allocate wasted votes

In using approval voting to elect multiple winners to a committee or council, it is desirable that excess votes—approvals beyond those that a candidate, especially a shoo-in, needs to win a seat—not

Satisfaction Approval Voting

We propose a new voting system, satisfaction approval voting (SAV), for multiwinner elections, in which voters can approve of as many candidates or as many parties as they like. However, the winners

Multiwinner approval voting: an apportionment approach

This work focuses on two divisor methods of apportionment, first proposed by Jefferson and Webster, that fall within a continuum ofapportionment methods and finds that the Webster apportionments tend to be more representative than the authors' based on Jefferson—by giving more voters at least one representative of whom they approve.

Sincerity and manipulation under approval voting

Under approval voting, each voter can nominate as many candidates as she wishes and the election winners are those candidates that are nominated most often. A voter is said to have voted sincerely if

Voting Systems that Combine Approval and Preference

This work proposes a way of combining PAV and FV in two hybrid voting systems, preference approval voting (PAV) and fallback voting (FV), that satisfy several desirable properties, including monotonicity.

Approval and plurality voting with uncertainty: Info-gap analysis of robustness

Voting algorithms are used to choose candidates by an electorate. However, voter participation is variable and uncertain, and projections from polls or past elections are uncertain because voter

The U.S. Electoral College and Spatial Biases in Voter Power

The United States does not provide for direct election of its chief executive but utilizes the Electoral College to represent voter choices. Central to this institution is the “winner-take-all” model



Mathematics and democracy : recent advances in voting systems and collective choice

Power Indices Taking into Account Agents' Preferences.- The Sunfish Against the Octopus: Opposing Compactness to Gerrymandering.- Apportionment: Uni- and Bi-Dimensional.- Minimum Total Deviation

Multiparty Democracy: Elections and Legislative Politics

Multiparty Democracy: Elections and Legislative Politics. By Norman Schofield and Itai Sened. New York: Cambridge University Press, 2006. 248p. $70.00 cloth, $24.99 paper. The elegant median voter

Democracy and the Market

From the instrumental point of view, the key to liberal democracy is some system of voting. Democracy and electoral competition are regarded as virtually synonymous, with interparty competition being

Just Elections: Creating a Fair Electoral Process in the United States

The 2000 election showed that the mechanies of voting, such as ballot design, can make a critical difference in the accuracy and fairness of our elections. But as Dennis F. Thompson persuasively

Electoral Engineering: Voting Rules and Political Behavior

Electoral Engineering: Voting Rules and Political Behavior. By Pippa Norris. Cambridge: Cambridge University Press, 2004. 390p. $70.00 cloth, $25.99 paper. Over 20 years ago, William Riker proposed

Collective Decisions and Voting: The Potential for Public Choice

Contents: Preface Part 1 Collective Decisions: Defining a collective decision A taxonomy of collective decision procedures Economic criteria for evaluating collective decisions General criteria for

Perspectives on public choice : a handbook

1. Public choice in perspective Dennis C. Mueller Part I. The Need for and Forms of Cooperation: 2. Economic theories of the state Russell Hardin 3. Neither markets nor states: linking transformation

Designing an all-inclusive democracy : consensual voting procedures for use in parliaments, councils and committees

Designing an All-Inclusive Democracy.- Collective Decision-making The Modified Borda Count, MBC.- A Pluralist Parliament for a Plural Society The Quota Borda System, QBS.- Electing a Power-sharing

Approval voting

Approval voting has been offered by a number of formal theorists, notably Steven Brams and Peter Fishburn (1983), as a solution to problems occasioned by multicandidate elections. The formal

Rules and Restraint: Government Spending and the Design of Institutions

Government spending has increased dramatically in the United States since World War II despite the many rules intended to rein in the insatiable appetite for tax revenue most politicians seem to