Professor H. L. Bray
Teaching
Math 89s:
Game Theory and Democracy
Fall Semester, August 25 -
December 3, 2026
Tuesdays and Thursdays, 4:40 - 5:55 p.m., Physics Building 205
Professor
Hubert Bray
bray@math.duke.edu
189 Physics Building
(919)757-8428 (mobile)
Office Hours: after class, and upon request
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 a particular class, 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 interpreted. 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.
On the weekend before your presentations, you will meet in groups to
practice your 5 minute presentations together. I also encourage you
to ask 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 Tuesday, August 25
The
Money and Politics Game
For Thursday, August 27
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 Tuesday, September 1
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 Thursday, September 3
1.07 The
Borda Count
1.08 The
Borda Count is NOT Clone Invariant
1.09 The
Borda Count and Nuclear War
For Tuesday, September 8
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 Thursday, September 10
Watch these videos:
1.13 Worst
Defeat
1.14 The
Schulze Method
1.15 Ranked
Pairs
For Tuesday,
September 15
Groups 3 and
4: Paper #1
(by midnight) and Presentation #1 (by the beginning of class)
For Thursday, September 17
Groups 1 and
2: Paper #1
(by midnight) and Presentation #1 (by the beginning of class)
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 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 Thursday, September 24
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 29
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 Thursday, October 1
Watch these videos:
2.01 The
Kelly Criterion: Triple or Nothing
2.02 The
Kelly Criterion: Quadruple or Nothing
For Tuesday, October 6
Groups 1 and 2: Paper #2 (by midnight) and Presentation #2 (by the
beginning of class)
For Thursday, October 8
Groups 3 and 4: Paper #2 (by midnight) and Presentation #2 (by the
beginning of class)
For Tuesday, October 13
No class today - Fall Break. No homework due either.
For Thursday, October 15
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 Tuesday, October 20
Watch these videos:
2.03 The
Gambler's Ruin
2.04 The
Kelly Criterion: The 0-1-2-3 Game
For Thursday, October 22
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 Tuesday, October 27
Groups 1 and 2: Paper #3 (by midnight) and Presentation #3
(by the beginning of class)
For Thursday, October 29
Groups 3 and 4: Paper #3
(by midnight) and Presentation #3 (by the beginning of class)
For Tuesday, November 3
Work any five problems from the textbook.
For Thursday, November 5
Work any five problems from the textbook.
For Tuesday, November 10
Work any five problems from the textbook.
For Thursday,
November 12
Work any five problems from the textbook.
For Tuesday, November 17
Groups 3 and 4: Paper #4 (by midnight) and Presentation #4
(by the beginning of class)
For Thursday, November 19
Groups 1 and 2: Paper #4 (by midnight) and Presentation #4 (by the
beginning of class)
Thanksgiving Break (no class on Tuesday, Nov. 24, since so many
people will be out of town)
For Tuesday,
December 1
The
Money and Politics Game
For Thursday, December 3
Free discussion.