MATH 1340: Mathematics and Politics

MATH 1340 is a course focusing on applications of mathematical reasoning to problems arising in the social sciences. Topics include voting systems and social choice, analysis of political power through power indices, game theory, fair division, and auction theory.

Textbooks

The course text is Mathematics and Politics: Strategy, Voting, Power, and Proof by Alan Taylor and Allison Pacelli. An electronic copy of the book is free for Cornell students, via the Cornell library.

Announcements

• The final exam will take place on Monday, May 22 at 7:00pm in Malott 253.
• Remember that you allowed to bring a 1-page (front and back) cheat sheet for Exam I.
• A friendly reminder that the first exam for the course will be in-class on Thursday, March 16.
• There will be no class on Thursday 02/23 and Tuesday 02/28.
• If you haven't done so already, sign up for the Piazza site and look at the first response question. When you've thought about the question and formulated a response you're happy with, post it under "Start a new followup discussion" in the "followup discussions" tab. Responses are due at the same time as the homework.
• For those of you still trying to get enrolled in the class, you need to get on the official MATH 1340 waiting list by talking to Heather in the math office on the 3rd floor of Malott. Tell them about any special circumstances that may give you higher priority (e.g. you are a senior and need the class to graduate).
• Here is the syllabus and the questionnaire from the first class. In case you missed the first class, please fill out and return the latter to me as soon as you can.
• The first class takes place on Thursday, January 26.

Homeworks

• Homework 1, due Thursday, February 2, Solutions.
• Homework 2, due Thursday, February 9, Solutions.
• Homework 3, due Thursday, February 16, Solutions.
• Homework 4, due Thursday, March 2, Solutions.
• Homework 5, due Thursday, March 9, Solutions.
• Practice Exam I, Solutions (use to study, will not be collected)
• Homework 6, due Thursday, March 23, Solutions.
• Homework 7, due Thursday, March 30, Solutions.
• Homework 8, due Thursday, April 13, Solutions.
• Homework 9, due Thursday, April 20, Solutions.
• Homework 10, due Thursday, April 27, Solutions.
• Homework 11, due Thursday, May 4, Solutions.
• Homework 12, due Thursday, May 11, Solutions.
• Practice Exam II, Solutions (use to study, will not be collected).

Topics covered

• Week 1 (01/26): Introduction to the course, "How is mathematics applicable to politics?", social choice functions [slides] (Ch. 1).
• Week 2 (01/31, 02/02): Examples of social choice functions and their properties, Example: 2009 Burlington, VT elections and the Condorcet paradox [slides] (Ch. 1).
• Week 3 (02/07, 02/09): Proving properties of social choice functions, "There is no perfect voting system," Yes-No voting systems and weighted systems (Ch. 1, 2).
• Week 4 (02/14, 02/16): "Is every yes-no voting system weighted?", swap robustness, trade robustness, elements of combinatorics (Ch. 2, 3).
• Week 5 (02/28, 03/02): Alternative ways to measure power, Shapley--Shubik and Banzhaf power indices (Ch. 3).
• Week 6 (03/07, 03/09): Calculating power indices, paradoxical aspects, Exam I review. (Ch. 3).
• Week 7 (03/14, 03/16): Winter Storm Stella, Exam I.
• Week 8 (03/21, 03/23): The chair's paradox, introduction to game theory, 2 x 2 ordinal games (Ch. 3-4).
• Week 9 (03/28, 03/30): Dominant strategies, Nash equilibria, the Brams--Wittman Theory of Moves (Ch. 4).
• Week 10 (04/11, 04/13): Iterated Prisoner's Dilemma, expected value, zero-sum games and mixed strategies (Ch. 4, 10).
• Week 11 (04/18, 04/20): The minimax theorem, the apportionment problem and apportionment methods, Balinski--Young theorem (Ch. 10, 5).
• Week 12 (04/25, 04/27): Fair division and notions of fairness (proportional, envy-free, equitable, efficient), fair division procedures (e.g. divide-and-choose, Austin's moving knife procedure, Adjusted Winner Procedure).
• Week 13 (05/02, 05/04): Dollar Auctions, Game Tree Analysis, O'Neill's theorem, auctions and bidding strategies (Ch. 6).
• Week 14 (05/09): Final exam review (Ch. 1-6, 10).

Back to Brian Hwang's home page.