Steven J. Brams is Professor of Politics at New York University and the author, co-author, or co-editor of 16 books and about 250 articles. His recent books include Theory of Moves (1994) and, co-authored with Alan D. Taylor, Fair Division: From Cake-Cutting to Dispute Resolution (1996) and The Win-Win Solution: Guaranteeing Fair Shares to Everybody (1999). His newest book, Mathematics and Democracy: Designing Better Voting and Fair-Division Procedures, appeared in 2008. Brams has applied game theory and social-choice theory to voting and elections, bargaining and fairness, international relations, and the Bible and theology. He is a former president of the Peace Science Society (1990-91) and of the Public Choice Society (2004-2006). He is a Fellow of the American Association for the Advancement of Science (1986), a Guggenheim Fellow (1986-87), and was a Visiting Scholar at the Russell Sage Foundation (1998-99).
Mathematics and Democracy: Designing Better Voting and Fair-Division Procedures
Democracy has two essential features: (1) periodic and fair elections and (2) rule of law and due process. With respect to (1), several alternatives to our present election system of plurality voting--with or without a runoff--have been proposed, including approval voting, single transferable vote, and the Borda count. I will offer an overview of these systems and discuss properties they do and do not satisfy. Feature (2) seems best achieved by fair-division algorithms that satisfy properties like "envy-freeness," whereby resources are divided so that everybody gets a share he or she considers comparable to that of others and so is not envious of them. I will illustrate difficulties one encounters in the fair division of divisible and indivisible goods, which may vitiate equal treatment of citizens under the law.