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.
Course Page: http://www.math.hmc.edu/~su/math188/

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".
Your paper should also contain a critical analysis of the methods used. For instance, does mathematics provide a good model for decision making in the context you describe? What's missing in the model? As people often make decisions based on such models, what would be appropriate or inappropriate uses of this model?

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.

HW Assignments
HW #1 (due Thu 9/1) READ YES, PLEASE READ
Straffin: Preface, Chapters 1, 7 and

Problem A. Fill out this Information Card. Then on your solutions for Problem B, indicate whether you have completed this task in Problem A.

Problem B. Find a short news article involving some sort of interaction or decision problem. Then, in just a few brief sentences:
(1) summarize the decision problem in the article,
(2) then identify each of the following: (a) the players, (b) some possible strategies for each player, (c) some possible aspects of conflict or cooperation between players.
(3) Staple a copy of the article to the back of your sheet.

Remember to write clearly and in complete sentences and explain your reasoning carefully. Good communication is important in this class. Be sure to read Writing Mathematics Well and do follow the Math Department's Homework Guidelines.

HW #2 (due Thu 9/8) READ YES, PLEASE READ
Straffin: Chapters 2, 7 and
Taylor: Preface, Sections 6.1-6.3.

DO Straffin Chapter 7 (3, 4, 5, 6abc, R6d).

"R" means READ and THINK about, but do not do the problem.

Boxing appropriate answers is helpful, but remember to write clearly and in complete sentences and explain your reasoning carefully. Good communication is important in this class. Be sure to read Writing Mathematics Well and do follow the Math Department's Homework Guidelines.

HW #3 (due Thu 9/15) READ Taylor Sections 4.1-4.3, AND Straffin Chapter 7.
"R" means READ and THINK about, but do not do the problem.
DO Straffin Chap.2 ( 1, 2, 3, R6, 7 ).
AND Taylor Chap. 4 ( 6 )
NOTE: Straffin has solutions to many problems in the back of the book. On your honor, I will allow you use them to check your solutions to just one of the problems (pick any one you like). Please do not use the solutions to look at any other problems.
HW #4 (due Thu 9/22) READ Straffin, Chapter 3.
DO Straffin Chap. 3 ( 1, 2, 3, 4, R5, 7 ).
NOTE: Straffin has solutions to many problems in the back of the book. On your honor, I will allow you use them to check your solutions to just one of the problems (pick any one you like). Please do not use the solutions to look at any other problems.
HW #5 (due Thu 9/29) READ Straffin, Chapter 4, 5, 6, 9. Taylor Chapter 10.
DO Straffin Chap.3 ( 5, R9 ) Chap.4 ( R2 ) Chap. 7 ( 6d ) 9 ( R1, 2, 3, 5 )

Don't forget: Friday Sept. 30 at 7pm in Galileo: Moody Lecture "Fractals and Chaos Games"!

HW #6 (due Thu 10/6) READ Taylor Chapter 4, Straffin Chapters 10, 11, 12.
DO Handout ( R21, 22, 23, 24 ) and
Straffin Chapter 10 ( R3 ), 12 ( 4, R6 ) and
Taylor Chapter 4 ( 13, R15, R23 )
HW #7 (due Thu 10/13) READ Straffin Chapters 16-17.
DO Handout Problems ( 7, R9, 11Y, 12Y, 15) AND
Problem C: Meet with 2 other people in the class. If you are a freshman, at least one of the other 2 people must be a senior. If you are a senior, at least one of the other 2 people must be a freshman. Discuss: (a) the ideas in the class that you have found most interesting and (b) ideas that you might want to pursue for your final course project. Write a paragraph about the ideas you discussed.
There is no homework due over Fall Break.
EXAM (due Thu 10/27) Note that the exam is due Thurs 10/27 in class unless special arrangements have been made with me.
Homework #8 (due Thu 11/3) READ Straffin Chapter 23, 25 and Taylor Chapter 2, 3. and
DO Straffin Chap. 23 ( 2, 3 ) 25 ( R1, 6 ) AND Taylor Chapter 2 ( 2, R3, 10 ) AND
PROBLEM D: Form a group of people you'd like to do the Final Project with, and begin to narrow down a topic. Ideally a team should have 3 people. Otherwise 2 or 4 could also work. Be sure to fill out this spreadsheet and describe who is in the group and what ideas you have discussed. Then indicate on your Homework that you have done Problem D so you can get credit for it.

(Guidelines for the Final Project are on the course website. A rough draft will be due before Thanksgiving, and course presentations will be scheduled after Thanksgiving.)

week of 11/10 Work on Course Projects
week of 11/17 Work on Course Projects
PAPER DRAFTS (due Tue 11/22) Each person should bring 2 copies of papers to class with you. Additionally, one person from each group should upload a copy of their paper draft to their Drop Box folder on Sakai.

We will be doing peer review of papers in class on Tuesday.