Professor H. L. Bray
        Teaching

Math 89s:
Game Theory and Democracy

Fall Semester, August 23 - December 1, 2021
Mondays and Wednesdays, 7:00 - 8:15 p.m.


Professor Hubert Bray                               bray@math.duke.edu
189 Physics Building                             (919)757-8428 (mobile)
Office Hours: after class, and upon request

Syllabus and Course Information

Welcome to the class! We're going to have a lot of fun together!

This is a DISCUSSON BASED class. I ask that you attend class every day. If you cannot attend, simply email me in advance of the class letting me know so that we may work out other arrangements.

Before many of the classes, I'm going to ask you to watch videos, as you can see below. Listen and learn with these videos as well as you can. Don't worry if you don't understand everything - that is not expected the first time. Just do your best and come to class with your questions!

However, make sure you do watch the videos. The daily quizzes are OPEN NOTES and will be easy for those who watched the videos, rewarding those who understood the simplest ideas. We'll pursue the deeper ideas in class. The whole point is to get the discussion going with the videos, so that we can cover some cool topics in class. Enjoy!

All quizzes, surveys, homeworks, papers, presentations, and other assignments will be turned in using GRADESCOPE.

You will write 4 papers in the class, each 5-10 pages, on a topic of your choice relating to the class, broadly interpretted. You will also present each topic to the class with a PowerPoint style presentation that lasts no more than 5 minutes. We'll discuss your topic ideas in class, so come to class with some ideas.

Our TA for the class is Keenan Powers <keenan.powers@duke.edu>. On the weekend before your presentations, you will meet with Keenan in groups to practice your 5 minute presentations together. I also encourage you to ask Keenan (and other students you make friends with) for feedback on your papers.

On your official presentation day, use gradescope to turn in your paper (by midnight) and your presentation (by the beginning of class). I encourage you to make your papers even better after class by taking the class discussion centered on your paper into account.


For Monday, August 23

Watch these videos:
1.01 Types of Ballots in Elections
1.02 Who Wins a Preferential Ballot Election?
1.03 Plurality and Instant Runoff Voting

For Wednesday, August 25

Watch these videos:
1.04 The Unit Interval Model
1.05 Instant Runoff Voting is NOT Monotone
1.06 The Margin of Victory Matrix

For Monday, August 30

Watch these videos:
1.07 The Borda Count
1.08 The Borda Count is NOT Clone Invariant
1.09 The Borda Count and Nuclear War

For Wednesday, September 1

Watch these videos:
1.10 Instant Runoff Borda is Condorcet
1.11 Instant Runoff Borda and the Unit Interval Model
1.12 The Game Theory of Condorcet Methods

For Monday, September 6

Watch these videos:
1.13 Worst Defeat
1.14 The Schulze Method
1.15 Ranked Pairs

For Wednesday, September 8

Watch these videos:
1.16 Comparison of Vote Counting Methods that use the Margin of Victory Matrix
1.17 What is Democracy?

For Monday, September 13

Groups 3 and 4: Paper #1 (by midnight) and Presentation #1 (by the beginning of class)

For Wednesday, September 15

Groups 1 and 2: Paper #1 (by midnight) and Presentation #1 (by the beginning of class)

For Monday, September 20

Survey at least 15 people on a question with at least 10 choices, such as "What is your favorite flavor of ice cream?" Print out 16 ballots, with instructions, which people can fill out by putting a 1 by their first choice, a 2 by their second choice, etc., and a 10 by their 10th choice. Fill out a 16th ballot yourself which you will designate the tie breaking ballot. Then go to www.wevotehere.org, click on "Create an Election" and then "Spreadsheet Election" and then follow the instructions. The web page will think for a few minutes and then return a spreadsheet which you can download which tells you which choice won the election according to Ranked Pairs, the ranking of all of the choices, as well as many other things about the election.

Turn in THREE things by gradescope by the beginning of class: The ballot you created, the spreadsheet produced by the web page, as well as a 1 page summary that you write which includes the question, the 10 choices (in order that they were ranked), and what you found interesting about the results. Did you find a Condorcet choice in each survey? Were there cycles in people's preferences? What surprised you or did not surprise you? Be prepared to discuss your survey in class.

Also, use this format for the files you turn in:

XYZ_Ice Cream Survey_Ballot.docx                    (or .pdf, or whatever)
XYZ_Ice Cream Survey_Computer Results.xlsx
XYZ_Ice Cream Survey_Summary.docx              (or .pdf, or whatever)

where XYZ represent your initials and you put the title of you survey where it says "Ice Cream Survey."

For Wednesday, September 22

Watch these videos:
2.01 The Kelly Criterion: Triple or Nothing
2.02 The Kelly Criterion: Quadruple or Nothing

For Monday, September 27

Survey at least 15 people on a question with at least 10 choices, such as "What is your favorite flavor of ice cream?" Print out 16 ballots, with instructions, which people can fill out by putting a 1 by their first choice, a 2 by their second choice, etc., and a 10 by their 10th choice. Fill out a 16th ballot yourself which you will designate the tie breaking ballot. Then go to www.wevotehere.org, click on "Create an Election" and then "Spreadsheet Election" and then follow the instructions. The web page will think for a few minutes and then return a spreadsheet which you can download which tells you which choice won the election according to Ranked Pairs, the ranking of all of the choices, as well as many other things about the election.

Turn in THREE things by gradescope by the beginning of class: The ballot you created, the spreadsheet produced by the web page, as well as a 1 page summary that you write which includes the question, the 10 choices (in order that they were ranked), and what you found interesting about the results. Did you find a Condorcet choice in each survey? Were there cycles in people's preferences? What surprised you or did not surprise you? Be prepared to discuss your survey in class.

Also, use this format for the files you turn in:

XYZ_Ice Cream Survey_Ballot.docx                    (or .pdf, or whatever)
XYZ_Ice Cream Survey_Computer Results.xlsx
XYZ_Ice Cream Survey_Summary.docx              (or .pdf, or whatever)

where XYZ represent your initials and you put the title of you survey where it says "Ice Cream Survey."

For Wednesday, September 29

Watch these videos:
2.03 The Kelly Criterion - The 0-1-2-3 Game
2.04 The Gambler's Ruin

For Wednesday, October 6

Survey two different groups of at leat 15 people on a question with at least 10 chioces. The goal will be to see if the two groups have different opinions on your question and, if so, what those differences are.

Turn in FOUR things by gradescope by the beginning of class:

XYZ_Ice Cream Survey_Ballot.docx                                        (or .pdf, or whatever)
XYZ_Ice Cream Survey_Computer_Results-Group 1.xlsx
XYZ_Ice Cream Survey_Computer_Results-Group 2.xlsx
XYZ_Ice Cream Survey_Summary.docx                                   (or .pdf, or whatever)

Discuss whatever you found interesting about the two surveys in one joint summary document. Did you find a Condorcet choice in each survey? Were there cycles in people's preferences? What surprised you or did not surprise you? Be prepared to discuss your survey in class.

For Monday, October 11

Groups 1 and 2: Paper #2 (by midnight) and Presentation #2 (by the beginning of class)

For Wednesday, October 13

Groups 3 and 4: Paper #2 (by midnight) and Presentation #2 (by the beginning of class)

For Monday, October 18

Work any five problems from the textbook.

For Wednesday, October 20

Survey two different groups of at leat 15 people on a question with at least 10 chioces. The goal will be to see if the two groups have different opinions on your question and, if so, what those differences are.

Turn in FOUR things by gradescope by the beginning of class:

XYZ_Ice Cream Survey_Ballot.docx                                        (or .pdf, or whatever)
XYZ_Ice Cream Survey_Computer_Results-Group 1.xlsx
XYZ_Ice Cream Survey_Computer_Results-Group 2.xlsx
XYZ_Ice Cream Survey_Summary.docx                                   (or .pdf, or whatever)

Discuss whatever you found interesting about the two surveys in one joint summary document. Did you find a Condorcet choice in each survey? Were there cycles in people's preferences? What surprised you or did not surprise you? Be prepared to discuss your survey in class.

For Monday, October 25

Work any five problems from the textbook.

For Wednesday, October 27

Work any five problems from the textbook.

For Monday, November 1

Groups 1 and 2: Paper #3 (by midnight) and Presentation #3 (by the beginning of class)

For Wednesday, November 3

Groups 3 and 4: Paper #3 (by midnight) and Presentation #3 (by the beginning of class)

For Monday, November 8

Work any five problems from the textbook.

For Wednesday, November 10

The Money and Politics Game

For Monday, November 15

Free discussion.

For Wednesday, November 17

Free discussion.

For Monday, November 22

Free discussion.

For Monday, November 29

Groups 3 and 4: Paper #4 (by midnight) and Presentation #4 (by the beginning of class)

For Wendesday, December 1

Groups 1 and 2: Paper #4 (by midnight) and Presentation #4 (by the beginning of class)