Math 89s:
Game Theory and Democracy

Fall Semester, 2018
Physics 227, Mondays and Wednesdays, 1:25 p.m. - 2:40 p.m.


Professor Hubert Bray                               [email protected]
189 Physics Building                             (919)757-8428 (mobile)

 Office Hours:  Mondays 2:40 – 3:10 and
                      Wednesdays 2:40 – 4:10


Syllabus and Course Information

Optional Material:  Additional Readings on Preferential Ballot Elections


Videos for this class are posted at https://professorbray.net/Videos/.

Take notes! You will be allowed to use your notes during your quizzes on these videos in class.


For Wednesday, August 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
1.04 The Unit Interval Model
1.05 Instant Runoff Voting is NOT Monotone

You will be quizzed on these videos in class on Wednesday.


For Monday, September 3, watch these videos:

1.06 The Margin of Victory Matrix
1.07 The Borda Count
1.08 The Borda Count is NOT Clone Invariant

You will be quizzed on these videos in class on Monday.
Take notes! The quiz is open notes and can cover anything we've done so far.

Also, as described in class, survey 15 people on a question with 15 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 15 by their 15th 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, the ranking of all of the choices, as well as many other things about the election.

Turn in THREE things to me by email, by class on Monday: 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 15 choices (in order that they were ranked), and what you found interesting about the results. 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 Wednesday, September 5, watch these videos:

1.09 The Borda Count and Nuclear War
1.10 Instant Runoff Borda is Condorcet
1.11 Instant Runoff Borda and the Unit Interval Model


For Monday, September 10, watch these videos:

1.12 The Game Theory of Condorcet Methods
1.13 Worst Defeat
1.14 The Schulze Method

Also, as described in class, survey two different groups of 15 people on a question with 15 chioces. The goal will be to see if the two groups have different opinions on your question and, if so, what those differences are. The files you will turn into me, by class on Monday, are

XYZ_Ice Cream Survey_Ballot.docx                                        (or .pdf, or whatever)
XYZ_Ice Cream Survey_Computer Results for Group 1.xlsx
XYZ_Ice Cream Survey_Computer Results for 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?


For Wednesday, September 12, watch these videos:

1.15 Ranked Pairs
1.16 Comparison of Vote Counting Methods that use the Margin of Victory Matrix
1.17 What is Democracy?


For Monday, September 24:

Paper 1 due, with 3 minute PowerPoint presentations in class.

Turn in your paper to me at [email protected] with "GTD" somewhere in your subject line, such as "GTD Paper 1." Your file should be named XYZ_Paper1_ShortTitle.docx (or .pdf, or whatever), where XYZ are your initials.


For Monday, October 1, watch these videos:

2.01 Balancing Risk and Reward in Investments
2.02 The Kelly Criterion: Quadruple or Nothing
2.03 The Gambler's Ruin

Take notes! There will be an open note quiz in class.


For Wednesday, October 3, watch these videos:

2.04 Kelly Criterion - Balancing Risk and Reward
4.01 Intro to General Relativity
4.02 The Geometry of Black Holes

Take notes! There will be an open note quiz in class.


For Monday, October 29:

Paper 2 due, with 3 minute PowerPoint presentations in class.

Turn in your paper to me at [email protected] with "GTD" somewhere in your subject line, such as "GTD Paper 2." Your file should be named XYZ_Paper2_ShortTitle.docx (or .pdf, or whatever), where XYZ are your initials.


For Monday, December 3:

Paper 3 due, with 3 minute PowerPoint presentations in class.

Turn in your paper to me at [email protected] with "GTD" somewhere in your subject line, such as "GTD Paper 3." Your file should be named XYZ_Paper3_ShortTitle.docx (or .pdf, or whatever), where XYZ are your initials.


For Monday, December 5:

Exam.