MA 103Q-002

Topics in Contemporary Mathematics: Mathematics and Politics

Mathematics

MA 103Q-002 Home Page

Basics

Semester: Spring 2004
Meeting time: MWF 9:10 - 10:00 a.m.
Meeting place: HA 266

Name: Stephen Schecter
E-mail address: schecter@math.ncsu.edu
Office location: Harrelson 349
Office hours: MWF 10:15 - 11, TH 9 - 10
Office telephone number: 515-6533
Office fax number: 515-3798

Apportionment of legislatures. Voting methods: fairness criteria and impossibility theorems. Use of game theory to analyze political dilemmas and strategies. Two Nobel prizes were awarded for material discussed in this course (Kenneth Arrow, 1972; John Nash, 1994).

MA 101 or equivalent.

Students will learn to develop, use, and analyze the limitations of mathematical methods for understanding and resolving political problems. In the process they will improve their ability to think critically. Specifically, students will


1. Learn different methods of apportioning legislatures and different voting methods.
2. Learn to use and criticize fairness criteria for apportionment and voting methods.
3. Learn to develop and criticize game theory models of political dilemmas.
4. Learn to use game theory techniques to analyze and develop strategies.
5. Learn to use and criticize some mathematical techniques for analyzing the distribution of political power.

Philip D. Straffin, Game Theory and Strategy, Mathematical Association of America, 1993, $38.95.

Coursepack of supplementary reading, $29.80.

Weeks	Topics	References
1 1/3	Apportionment of legislatures	For All Practical Purposes, chapter 15 (coursepack)
1 1/3	Voting methods	For All Practical Purposes, chapter 12 (coursepack)
1	2-person zero-sum games	Straffin, chapters 1 - 3
1	Game trees	Straffin, chapter 7. "Political Intrigue in the Bible: Esther" from Brams, Rational Politics, chapter 2 (coursepack).
2/3	Review (Mon. Feb. 16), Test 1 (Wed. Feb. 18)
1/3	Utility	Straffin, chapter 9
2	2-person non-zero-sum games, Nash equilibria, Pareto optimality, Chicken, Prisoners' Dilemma, promises and threats	Straffin, chapters 11 - 12, 14. The White House Tapes and the Cuban Missile Crisis, in Brams, Rational Politics, pages 157 - 167 and chapter 6 (coursepack).
2/3	Evolution of strategy	Straffin, chapter 15
1/3	Nash arbitration scheme	Straffin, chapter 16
2	n-person games, strategic voting, tragedy of the commons, Pathan tribal organization	Straffin, chapters 19 - 21, 24
2/3	Review (Mon. Apr. 5), Test 2 (Wed. Apr. 7)
2	Shapley value, power in weighted voting systems	Straffin, chapters 26 - 28. For All Practical Purposes, chapter 13 (coursepack).
1	Review

Here are the review sheets for Test 1 and Test 2.

Here is the review sheet for the final exam. The final exam is Monday, May 10, 8 - 11 a.m., in the usual room.

There will be three 3 - 5 page papers.


• Paper 1, due Monday, Mar. 1 (not Friday, Feb. 27, as originally announced), on one of the following:
  
  
  • Congressional staffer's report on whether the current method of apportioning the U.S. Congress should be changed and, if so, to what.
    
    
  • Legislative staffer's report on whether the current method of electing North Carolina state officials should be changed and, if so, to what.
    
    
  • A topic of your choice approved in advance by the instructor.
    
    
  Details are here.
  
  
• Paper 2, due April 5. Model a political or interpersonal situation as a 2-person game. Describe the strategies available to each player, the outcomes that would result from each pair of strategies, and how the players would rank these outcomes. What is the likely result of this game? Criticize your model, describing both useful insights that it yields and ways in which it might be misleading. (Possible situations to use in this paper will be given; others can be proposed by the student and approved by the instructor.) Details are here.
  
  
• Paper 3, due Friday, Apr. 30. Details are here.

Attendance at all meetings of the class is expected. Occasional absences will be approved if they meet University policy (see University policies, items 1 and 2).

• Attendance and class participation 10%
• Three 3 - 5 page papers 30%
• Two in-class tests 30%
• Final exam 30%

The NC State policy on working with students with disabilities can be found here.

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