MATH 188 --- Social Choice and Decision Making
Fall 2011
Professor Francis Su
Olin 1269, 607-3616
my-last-name@math.hmc.edu

People make decisions everyday --- small ones such as what to eat or wear, to large ones such as which job to take or whether to buy a house. Groups of people also make decisions, such as which president to elect, or what policies to adopt, what business strategies to pursue. Mathematics has much to offer the decision-maker --- both in the analysis of strategies and suggestions for a course of action.

In this course, we will focus on the modeling of individual and group decisions using mathematical techniques from "game theory", the area of mathematics that was pioneered in the 1950's by John Nash and others, but now has applications to a wide variety of disciplines: economics, biology, computer science.

Topics will include: basic concepts of game theory and social choice theory, representations of games, Nash equilibria, utility theory, non-cooperative games, cooperative games, voting games, paradoxes, Arrow's impossibility theorem, Shapley value, power indices, "fair division" problems, and applications.

This course has substantial overlap with Math 155, so Math 188 and Math 155 cannot both be counted for credit. This is an HMC Integrative Experience course, meaning that it explores the interaction between science, technology, and society.

Lectures: TTH 8:10-9:25pm, Location: Beckman B134

Office Hours: Tuesdays 4-5pm, Wednesdays 1:30-2:30pm, or by appt: Olin 1269.

Required Texts:

• Phil Straffin, Game Theory and Strategy.
• Alan Taylor and Allison Pacelli, Mathematics and Politics.

Lectures: Attendance and doing the assigned reading will be essential for success in the course.
Homework: There will be weekly homeworks, announced on the course homepage, and due Thursdays in class. You may discuss homework problems with others, but you must write them up individually. Identical homeworks will not receive credit. No late homeworks except in unusual circumstances. You will be able to drop one assignment.
Exams: 1 midterm (tentatively scheduled Fri 10/21) and a final exam.
Grading: Homework, Midterm, Final Project, and Final Exam are each worth 25%. The grader for the course is Michael Earnest.

Writing Project: As this is an Integrative Experience course, there will be a paper and an oral presentation involving a critical analysis of the relationship of the mathematical methods of game theory to contemporary society. This will be a group project. In your paper and presentation, you'll model a real-life situation of your choice using the techniques of decision analysis and game theory, or choose an existing model in the literature to critique. Some examples could include:

• I. Choose a past historical event or situation, model the agents and strategies involved, and use your model to explain why events transpired the way they did.
  • Ex. Division of post-war Germany
  • Ex. Intervention of 3rd party candidates in nat'l elections
  • Ex. Predator-prey relationships in biological ecosystems
• II. Choose a current situation or event, model the agents and strategies involved, and then use your model to (a) suggest a course of action or (b) make a prediction about what will happen
  • Ex. marketing strategies for a new business
  • Ex. the Palestinian conflict
  • Ex. strategies to contain the spread of AIDS
• III. Choose a current social choice problem and understand it in terms of ideas from cooperative game theory.
  • Ex. coalition formation in an organization
  • Ex. analysis of the power structure in a business or organization
  • Ex. resource allocation and "fair division".

Writing Center: the friendly folk there can help you with your writing! The Writing Center provides a good opportunity for you to get feedback on your work at each stage of the writing process, from working out ideas to polishing a final draft. This is a resource that can be helpful to all writers, from novices to experts, on all kinds of writing. The center is open Sunday through Thursday evenings from 7-11 and Saturday afternoons from 3-5. It is located in Parsons 161 in the basement just off the Galileo foyer. You may schedule an appointment through their website, http://www.hmc.edu/writingcenter/, or you may simply drop in during normal hours. If you'd like an appointment outside of normal hours, you may e-mail writing_center@hmc.edu with your request. You are likely to find your writing center visit more valuable if you come earlier than the night before the paper is due.