Professor H. L. Bray
        Teaching

Math 190s-02m:
Game Theory and Democracy

Summer Term 1, May 13 - June 6, 2020
Monday - Tuesday - Wednesday - Thursday - 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

Syllabus and Course Information

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 3 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 each Thursday, so come to class with some ideas. You'll then have Fridays and Saturdays to write your paper (roughly), with a rough draft due by midnight each Saturday. On Sundays you'll create your 5 minute presentations which you can practice in group meetings on Sundays with the TA (Sam Lester, a 2020 Duke graduate, and former president of the Duke Univ. Marching Band). You will then give your official 5 minute presentation in class on Mondays, with the final version of the paper due on Mondays by midnight (except Memorial day - which is a Monday, so everything is due Tuesday).


For Wednesday, May 13

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, May 14

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, May 15

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 Monday, May 18

Email papers (by midnight) and presentations (by the beginning of class) to bray@math.duke.edu and samuel.lester@duke.edu.

For Tuesday, May 19

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 Wednesday, May 20

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

For Thursday, May 21

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

For Friday, May 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.

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 Monday, May 25

Memorial Day Holiday - no class

For Tuesday, May 26

Email papers (by midnight) and presentations (by the beginning of class) to bray@math.duke.edu and samuel.lester@duke.edu.

For Wednesday, May 27

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, May 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 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, June 1


Email papers (by midnight) and presentations (by the beginning of class) to bray@math.duke.edu and samuel.lester@duke.edu.

Saturday, June 6, 2020

FINAL EXAM from 2 p.m. to 5 p.m.