Professor H. L. Bray
Teaching
Math 190s-02m:
Game Theory and Democracy
Summer Term 2, June 29 - August 5, 2020
Monday - Wednesday - Friday, 2:00 - 4:05 p.m.
Professor
Hubert Bray
bray@math.duke.edu
189
Physics Building
(919)757-8428 (mobile)
Office
Hours: after class, upon request
TA: Sam Lester, samuel.lester@duke.edu
Welcome
to the class! We're going to have a lot of fun together. Unlike most
math classes, these classes are discussion based. Furthermore, the
topics we cover will have a lot to do with the questions you ask in
class, so bring your favorite questions!
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. Rough drafts of your papers are due to the TA of the
class (Sam Lester, a former student) 2 days before the due date so that
he can give you feedback. You will also meet with students in groups
the day before your presentations to practice your presentations with
each other. This is all to set you up for success on your presentation
day when both your paper and your presentation are due by midnight to
both bray@math.duke.edu and samuel.lester@duke.edu.
For Monday, June 29
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, July 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 Friday, July 3
No class - University wide holiday.
For Monday, July 6
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, July 8
Email papers (by midnight) and presentations (by the beginning of class) to bray@math.duke.edu and samuel.lester@duke.edu.
For Friday, July 10
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, July 13
Watch these videos:
1.13 Worst Defeat
1.14 The Schulze Method
1.15 Ranked Pairs
For Wedneday, July 15
Watch these videos:
1.16 Comparison of Vote Counting Methods that use the Margin of Victory Matrix
1.17 What is Democracy?
For Friday, July 17
Email papers (by midnight) and presentations (by the beginning of class) to bray@math.duke.edu and samuel.lester@duke.edu.
For Monday, July 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.
If you have any problems at all, our TA, Sam Lester, samuel.lester@duke.edu, is very happy to help you!
Turn in THREE things by email to bray@math.duke.edu and samuel.lester@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 Wedneday, July 22
Watch these videos:
2.01 The Kelly Criterion: Triple or Nothing
2.02 The Kelly Criterion: Quadruple or Nothing
2.03 The Kelly Criterion - The 0-1-2-3 Game
2.04 The Gambler's Ruin
For Friday, July 24
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 and samuel.lester@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 Monday, July 27
Email papers (by midnight) and presentations (by the beginning of class) to bray@math.duke.edu and samuel.lester@duke.edu.
For Wednesday, July 29
Homework assigned in class is due.
For Friday, July 31
Homework assigned in class is due.
For Monday, August 3
Homework assigned in class is due.
For Wednesday, August 5
Email papers (by midnight) and presentations (by the beginning of class) to bray@math.duke.edu and samuel.lester@duke.edu.