Professor H. L. Bray
        Teaching

Math 89s:
Game Theory and Democracy

Fall Semester, August 17 - November 24, 2020
Tuesdays and Thursdays, 3:30 - 4:45 p.m.


Professor Hubert Bray                               bray@math.duke.edu
189 Physics Building                             (919)757-8428 (mobile)
Office Hours: after class, 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. Even though this is an online class, I ask that everyone attend class every day with their cameras on. 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!

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.

Everyone will be assigned to a group of around 4 students to meet with outside of class. Groups will meet both 2 days before your official presentation day and 1 day before your official presentation day, on a schedule that you work out with each other.

Rough drafts of your papers are due to your student group (email each other) 2 days before your official presentation day so that you may give each other feedback (over Zoom). You will practice your presentations with your student group (over Zoom) 1 day before your official presentation day.

On your official presentation day, email your paper (by midnight) and your presentation (by the beginning of class) to bray@math.duke.edu. I encourage you to make your papers even better after class by taking the class discussion centered on your paper into account.


For Tuesday, August 18

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 Thursday, August 20

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 Tuesday, August 25

 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 Thursday, August 27

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 Tuesday, September 1

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

For Thursday, September 3

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

For Tuesday, September 8

Groups 3 and 4: Email your paper #1 (by midnight) and your presentation #1 (by the beginning of class) to bray@math.duke.edu. Make sure you have "GTD" in the subject headline, as with any assignments you turn in to me.

For Thursday, September 10

Groups 1 and 2: Email your paper #1 (by midnight) and your presentation #1 (by the beginning of class) to bray@math.duke.edu. Make sure you have "GTD" in the subject headline, as with any assignments you turn in to me.

For Tuesday, September 15

 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 email to bray@math.duke.edu 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?

Put "GTD" in your email subject headline so that I know this is homework you are turning in. Be prepared to discuss your survey in class.

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

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 Thursday, September 17

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

For Tuesday, September 22

 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 email to bray@math.duke.edu 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?

Put "GTD" in your email subject headline so that I know this is homework you are turning in. Be prepared to discuss your survey in class.

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

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 Thursday, September 24

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

For Tuesday, September 29

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 email to bray@math.duke.edu 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?

Put "GTD" in your email subject headline so that I know this is homework you are turning in. Be prepared to discuss your survey in class.

For Thursday, October 1

Work any five problems from the textbook and email them to me before class.

For Tuesday, October 6

Groups 1 and 2: Email your paper #2 (by midnight) and your presentation #2 (by the beginning of class) to bray@math.duke.edu. Make sure you have "GTD" in the subject headline, as with any assignments you turn in to me.

For Thursday, October 8

Groups 3 and 4: Email your paper #2 (by midnight) and your presentation #2 (by the beginning of class) to bray@math.duke.edu. Make sure you have "GTD" in the subject headline, as with any assignments you turn in to me.

For Tuesday, October 13

Groups 1 and 2: Email your paper #3 (by midnight) and your presentation #3 (by the beginning of class) to bray@math.duke.edu. Make sure you have "GTD" in the subject headline, as with any assignments you turn in to me.

For Thursday, October 15

Groups 3 and 4: Email your paper #3 (by midnight) and your presentation #3 (by the beginning of class) to bray@math.duke.edu. Make sure you have "GTD" in the subject headline, as with any assignments you turn in to me.

For Tuesday, 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 email to bray@math.duke.edu 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?

Put "GTD" in your email subject headline so that I know this is homework you are turning in. Be prepared to discuss your survey in class.

For Thursday, October 22

Work any five problems from the textbook and email them to me before class.

For Tuesday, October 27

Work any five problems from the textbook and email them to me before class.

For Thursday, October 29

Work any five problems from the textbook and email them to me before class.

For Tuesday, November 3

US election themed survey results due, as discussed in class.

For Thursday, November 5

No homework. You deserve a break! Brainstorm on your next paper and presentation, if you like.

For Tuesday, November 10

Groups 3 and 4: Email your paper #4 (by midnight) and your presentation #4 (by the beginning of class) to bray@math.duke.edu. Make sure you have "GTD" in the subject headline, as with any assignments you turn in to me.

For Thursday, November 12

Groups 1 and 2: Email your paper #4 (by midnight) and your presentation #4 (by the beginning of class) to bray@math.duke.edu. Make sure you have "GTD" in the subject headline, as with any assignments you turn in to me.