Mathematics and Democracy: Designing Better Voting and Fair-Division Procedures

Steven J. Brams

ທ.ວ. 2009 · Princeton University Press

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Voters today often desert a preferred candidate for a more viable second choice to avoid wasting their vote. Likewise, parties to a dispute often find themselves unable to agree on a fair division of contested goods. In Mathematics and Democracy, Steven Brams, a leading authority in the use of mathematics to design decision-making processes, shows how social-choice and game theory could make political and social institutions more democratic. Using mathematical analysis, he develops rigorous new procedures that enable voters to better express themselves and that allow disputants to divide goods more fairly.


One of the procedures that Brams proposes is "approval voting," which allows voters to vote for as many candidates as they like or consider acceptable. There is no ranking, and the candidate with the most votes wins. The voter no longer has to consider whether a vote for a preferred but less popular candidate might be wasted. In the same vein, Brams puts forward new, more equitable procedures for resolving disputes over divisible and indivisible goods.

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Steven J. Brams is professor of politics at New York University. He is the author of Theory of Moves, among many other books, and the coauthor of The Win-Win Solution: Guaranteeing Fair Shares to Everybody and Fair Division: From Cake-Cutting to Dispute Resolution.