Math 89s:
Game Theory and Democracy

Fall 2019
Physics 227, Tuesdays and Thursdays, 10:05 - 11:20 a.m.


Professor Hubert Bray                               bray@math.duke.edu
189 Physics Building                             (919)757-8428 (mobile)
Office Hours: after class, upon request
www.professorbray.net

More course information is listed at the bottom of the page.


For Thursday, 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


For Tuesday, September 3

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 5

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 Tuesday, September 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 Thursday, September 12

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


For Tuesday, September 17

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


For Thursday, September 19

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 Tuesday, September 24


Papers and presentations due.

By 6 p.m. the previous evening, email your paper to me at bray@math.duke.edu with email subject "GTD" so that I know this is homework you are turning in. The filename of your paper should be in the form XYZ_Paper1_ShortTitle.docx (or .pdf, or whatever), where XYZ are your initials.

Be sure to practice your presentations on your papers, which may not last more than 3 minutes, with 1 minute for questions. You will be cutoff after 3 minutes since otherwise there will not be enough time for everyone to present.


For Thursday, September 26


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 according to Ranked Pairs, 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. 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 Tuesday, October 1


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?

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 Tuesday, October 29

Papers and presentations due.

By 6 p.m. the previous evening, email your paper to me at bray@math.duke.edu with email subject "GTD" so that I know this is homework you are turning in. The filename of your paper should be in the form XYZ_Paper2_ShortTitle.docx (or .pdf, or whatever), where XYZ are your initials.

Be sure to practice your presentations on your papers, which may not last more than 3 minutes, with 1 minute for questions. You will be cutoff after 3 minutes since otherwise there will not be enough time for everyone to present.


For Tuesday, December 3

Papers and presentations due.

By 6 p.m. the previous evening, email your paper to me at bray@math.duke.edu with email subject "GTD" so that I know this is homework you are turning in. The filename of your paper should be in the form XYZ_Paper2_ShortTitle.docx (or .pdf, or whatever), where XYZ are your initials.

Be sure to practice your presentations on your papers, which may not last more than 3 minutes, with 1 minute for questions. You will be cutoff after 3 minutes since otherwise there will not be enough time for everyone to present.


For Thursday, December 5

Final Comprehensive Quiz


_______________________________________________________________


Course Objectives:
What is democracy? For example, given a finite number of choices, how does a group of equals choose the
option which “best” reflects the will of the group? When there are more than two options, this is an open
question in the sense that philosophical notions of “best” are not universally agreed upon. In this seminar, we
will use mathematics and game theory to aid us in our discussion on the meaning of democracy and to examine
the pros and cons of different approaches to this question. We will discuss preferential ballot elections (where
each voter ranks all of the choices) and cover some of the most common vote counting methods used to
determine a winner in a preferential ballot election. We will see how some of the most “obvious” vote counting
methods, such as Instant Runoff Voting (used on many college campuses), have some significant theoretical
defects. The seminar will also include an introduction to game theory, both for its own sake, as well as an
essential tool for predicting how intelligent people with agendas behave given carefully defined rules.

Quizzes:
Most classes will begin with a quiz over material already covered in class as well as videos assigned to watch
outside of class.

Homework:
Students will conduct and analyze surveys and elections. Problems will also be assigned in class.

Papers:
Each student will write three papers (5-10 pages) on the topics of their choice which make connections to game
theory and democracy.

Final Exam:
Students will be tested on all of the material presented in class, except other students’ presentations.

Grading:
45% Final Comprehensive Quiz
30% Quizzes and Homework
15% Three papers and presentations.
10% Class Participation

Most Important Dates:
Tuesday, September 24, 2019 – 1st paper due.
Tuesday, October 29, 2019 – 2nd paper due.
Tuesday, December 3, 2019 – 3rd paper due.
Thursday, December 5, 2019 – Final comprehensive quiz on the last class.

If you will not be present for any of these dates, please notify me well in advance, if possible.