Mathematics and Politics

Registration Fee: $325 by May 5, $450 after

The field of Mathematics and Politics seeks to answer questions arising in political science from a mathematical perspective. For example:

• Who should have won the 2000 presidential election, and—more generally—what are the best voting procedures to use when there are three or more candidates?
• What fraction of power does the president have in the US Federal System, and—more generally— how does one measure political influence in legislative systems?
• How can marital assets be divided fairly, and how is this related to the resolution of international disputes?

Many questions like these can be answered with little or no background in either mathematics or political science. The accessibility of the material, therefore, makes it a perfect backdrop to introduce mathematical reasoning to undergraduates in the humanities and social sciences, giving them the opportunity to investigate active areas of mathematics research and refine their critical thinking skills in a setting that is largely noncomputational.

This workshop will introduce several areas of mathematics and politics, including escalation, conflict, voting systems (including Arrow’s Impossibility Theorem and the Gibbard-Satterthwaite Manipulability Theorem), power, fair division of divisible and indivisible goods, and apportionment. Participants will develop the tools needed to introduce such topics to their students, by either enriching courses with new material or by developing a new course devoted entirely to the subject in as early as the fall of 2008. There is also an abundance of material here that mathematics majors will find interesting and challenging as well. Participants will be provided with some reading materials and related questions to think about before the workshop.

More information regarding the workshop can be found online at http://www.williams.edu/mathematics/apacelli/MAA_PREP_2008.html.