Math 89s - Game Theory and Democracy
Fall 2017

Tuesdays and Thursdays, 10:05 - 11:20 a.m., Physics 227

Hubert Bray, Professor of Mathematics and Physics, Duke University
Office Hours:  Mondays, 5:00 - 7:00 p.m.
(Please email me if you are coming after 5:30 p.m. so that I will know not to leave early.)

Course Information

Senior Theses and Additional Readings        

Important Due Dates:

September 14: Come to class with the first paragraph of your first paper.

October 5: Paper #1 is due.

November 30: Paper #2 is due.

December 7: Exam (in class) 

Specific Instructions (for your two papers):
1. Pick a topic that interests you that relates to game theory, democracy, or both. The audience is your fellow classmates.
2. Make your topic very specific so that you have a chance to cover it in detail.
3. Find at least 3 major sources (academic papers, books) that you use in a major way throughout your paper.


4. Be precise so that the reader understands your points. Define and explain terms that everyone might not already know.
5. Go to the library and talk to a librarian who can give you help finding sources.
6. Consider using Duke's Writing Studio, where you can find someone to help you with your paper.


Thursday, August 31:  Poll 15 friends on a controversial multiple choice question with 4-6 choices.
Tuesday, September 5:  Analyze your poll using
  1. Plurality
  2. Instant Runoff Voting
  3. The Borda Count
  4. Instant Runoff Borda
  5. Worst Defeat
    Also compute the margin of victory matrix and the Condorcet winner, if there is one.

Thursday, September 7: Analyze your poll using

Tuesday, September 12:

1. Email me 4 things:
1. Your blank ballot (scan it if it is not already digital) that you gave each voter to fill out.
2. The spreadsheet of votes you entered into
3. The spreadsheet produced by
4. A short summary of your poll containing your survey question and possible answers, the winners by each of the six methods (Plurality, IRV, Borda, IR Borda, WD, Ranked Pairs), whether or not there was a Condorcet winner, and a brief analysis of the election and which choice is the most legitimate winner.

2. Make sure your name does appear in any of the documents you send me. Delete your name, wherever your name appears. Also, delete any other identifying information. This is to protect your privacy from random people who view your election results on the web.

3. Use this PRECISE format for your file names, where you replace ABC with your initials (or any 3 letter code that you want to represent you) and you replace "Ice Cream" with a short title for your survey:
1. ABC_Ice Cream_Ballot.docx (or .pdf, .png, .jpg, ...)
2. ABC_Ice Cream_Votes.xlsx
3. ABC_Ice Cream_Results.xlsx
4. ABC_Ice Cream_Summary.docx

Thursday, September 14:  Read this essay and come to class with your first paragraph for your proposed paper, to discuss with Professor Astrid Giugni.

Tuesday, September 19:
Here are the two websites you'll need to communicate with Professor Giugni's class:


1. Be sure to "Accept Invite" in the email I sent you. This will allow you access to the english89s_03_f2017 folder within your box at website (1).

2. Watch the videos that show up in the folder. These videos summarize what the other class has been learning.

3. At website (2), first click on the tab "Presentation Feedback Guidelines" and read the information. Then click on the tab "Presentation One-Machiavelli" and follow the instructions on how to leave your feedback.

Leave feedback for this first video by class on Tuesday.

Tuesday, September 26:
Listen to the 2nd video made by Professor Giugni's class and leave a thoughtful comment on the web page, as you did for the first video.

Tuesday, October 5:
Please follow these precise instructions to turn in your paper by midnight tonight:

1. Do NOT include your name anywhere in the paper.
2. Your file name should have the form ABC_Paper1_ThisIsMyBriefTitle.pdf where ABC are your initials. Do not use any spaces, and capitalize the first letter of each word in your title.
3. Email your paper as an attachment to

Tuesday, October 18:
Read the textbook for the course that I emailed to you. Try to understand the main ideas of the book, and pick a couple of topics in the book to study in detail. Bring your questions to class on Tuesday.

Tuesday, October 25:
1) Work any 6 problems from the textbook (that I emailed you). The problems are located throughout the textbook, so part of the HW is finding the problems. Continue skimming the textbook.

2) Read 9 of your fellow students' papers, and write down comments (not to be turned in) for each paper. Think about how you can make your next paper better by incorporating some of the successful ideas used by your fellow classmates.