MAT 306: Mathematics & Politics — Strategy, Voting, Power & Proof

13 April 2004 — 16 April 2004

Old Main 403 from 5pm — 8:30pm Daily

Instructor:   Alan D. Taylor
Marie Louise Bailey Professor of Mathematics
Department of Mathematics
Union College
Schenectady, NY

Course Outline: About two thirds of this course will be based on my text Mathematics and Politics (Springer-Verlag, 1995). The remainder of the class time will focus on material from my two recent books with Steven Brams of New York University’s Department of Politics; one is entitled Fair Division: From Cake Cutting to Dispute Resolution (Cambridge, 1996), and the other is entitled The Win-Win Solution: Guaranteeing Fair Shares to Everybody (Norton, 1999). Specific topics to be covered from these three texts will include the following:

Escation and Auction

The dollar auction
Game-tree analyses
Back-of-the-envelope calculations
O’Neill’s theorem
Vickery auctions and eBay

Game Theoretic Models Of International Conflict

Dominant strategies and Nash equilibria
Prisoner’s dilemma and chicken
The arms race, the Cuban missile crisis, and the Yom Kippur war
The theory of moves

Fair Division and Dispute Resolution

Discrete schemes for the cake-cutting metaphor
Moving-knife schemes for the cake-cutting metaphor
Adjusted winner
Real-world applications
Taking turns

Voting Theory

May’s theorem for two alternatives
Concrete voting procedures
Desirable properties
Condorcet’s paradox and the chair’s paradox
Arrow’s impossibility theorem
Manipulability

Biographical Information: Prof. Taylor is currently the Marie Louise Bailey Professor of Mathematics at Union College, an endowed Chair. Taylor is the author of five books, several book chapters, and numerous papers. Recently he has written two high profile texts with political scientist Steven Brams (New York University) on fair division. The work of Brams and Taylor has been the focus of articles in the London Times (front page, 15 July 1999), the New York Times (7 August 1999), the New Yorker, New Scientist, Newsweek, and Fortune Magazine.

Prof. Taylor has been the recipient of four NSF research grants and in 1998 he was winner of the Stillman Prize for Teaching. A brilliant speaker, Taylor has given compelling lectures and workshops at Canisius College in the past.