Instructor: Carissa Slone
Office Hours: Mondays 12-2pm, Hylan 820
Email: cslone2 (at) ur (dot) rochester (dot) edu
Textbook: Taylor and Pacelli, Mathematics and politics. Strategy, voting, power and proof. Second edition. Springer, New York, 2008.
Topics Covered: Conflict with ordinal Game Theory, including elementary applications (Nash equilibria, Prisoner’s Dilemma political situations) and Brams’ Theory of Moves. Measures of voting power (including the Banzhaf and Shapley-Shubik indices), Chair’s Paradox, ordinal measures of power, escalation, Vickrey auctions, social choice (including Arrow’s Theorem and Sen’s Theorem), Yes-No voting systems. Depending on time available, other topics may be treated, such as apportionment.
Homework: There will be weekly homework assignments, due each Friday at 11:59pm on Gradescope.
Exams:
Midterm -- in class on Wednesday, Oct 26
Final -- in Meliora 224 (regular classroom) on Monday, Dec 19 at 4:00pm
Grading:
Homework 30%
Midterm Exam 30%
Final Exam 40%
Necessary Background: Officially, there are no prerequisites for this course. However, knowledge of high school algebra will be used throughout the course and in general, mathematical maturity (i.e., some familiarity with making mathematical arguments) is helpful. As the course progresses, we will learn techniques that will enable us to make sophisticated logical arguments, and as with anything, this will get easier as things go along and one gets more familiarity with the concepts. Developing this ability is important as it augments the learning of the practical techniques and develops the critical thinking needed to apply the material efficiently in other areas of study and work.
What to Expect: This is a reasonable class. As long as you keep up with the lectures, do the homework and figure out what you did wrong on any mistakes, then the exams should not be too much of a problem. (If you study for them!) Here are a couple of things that might scare you. First, you’ll have to do simple proofs once in a while. All I can tell you is that this is a good course to start to get a basic idea of how to do mathematical proofs. If you ever need any ideas or help on anything, please don’’t be shy to attend to my office hours.
Homework Policy: Late homework will be accepted up to one week post due date (e.g., homework due on Oct. 7 can still be submitted up to 11:59pm on Oct. 14). However, there will be a 50% reduction in the points earned on the homework (Say 10 points are earned, then only 5 will be counted). Any homework submitted after the one week period will receive a 0.
Disability Support: If you have an academic need related to a disability, arrangements can be made to accommodate most needs. For information please contact the Center for Excellence in Teaching and Learning. Note: To be granted alternate testing accommodations, you (the student) must fill out forms with CETL at least seven days before each and every exam. These forms are not sent automatically. Professors are not responsible for requesting alternative testing accommodations at CETL, and they are not obligated to make any accommodations on their own.
Academic Integrity Statement: You are responsible for knowing and abiding by the University of Rochester’s academic integrity code. For a complete listing visit the College of Arts, Sciences, and Engineering’s web site. Any violation of academic integrity will be pursued according to the specified procedures. In particular, submission of written work, including homework and exams, which has been copied from the work of other students (or anyone else) with or without their knowledge or consent, is plagiarism.
If slides are not linked for a particular day, then that day is an in-class homework day.
Week of Aug 31 (Week 1):
Topic: Introduction and 1.1-1.4
Week of Sept 5 (Week 2):
Topic: Social Choice
Reading: 1.1-1.8
Homework 1. Ch. 1: 4, 6, 12, 13, 23 (due Friday, Sept 23 at 11:59pm)
Week of Sept 12 (Week 3):
Topic: Yes-No Voting
Reading: 2.1–2.6
Homework 2. Ch. 2: 4, 8, 10, 14, 18, 19, 22 (due Wednesday, Sept 28 at 11:59pm)
Week of Sept 19 (Week 4):
Topic: Shapley-Shubik Power Index
Reading: 3.1–3.3
Homework 3. Ch. 3: 9, 10, 12, 22(b), 23(b), 26(a) (due Friday, Sept 30 at 11:59pm)
Week of Sept 26 (Week 5):
Topic: Banzhaf Power Index, Chair's Paradox
Reading: 3.4–3.7
Homework 4. Ch. 3: 22(a), 23(a), 26(b), 29, 36, 38, 42 (due Friday, Oct 7 at 11:59pm)
Monday slides. Wednesday slides.
Week of Oct 3 (Week 6):
Topic: Games, Nash Equilibria, Prisoner's Dilemma, Chicken
Reading: 4.1–4.5
Homework 5. Ch. 4: 3-6, 10, 14 (due Friday, Oct 14 at 11:59pm)
Week of Oct 10 (Week 7):
Topic: Yom Kippur War and the Theory of Moves
Reading: 4.6–4.7
Homework 6. Ch. 4: 23, 33-35 (due Friday, Oct 21 at 11:59pm)
FALL BREAK (Oct 10-11)
Week of Oct 17 (Week 8):
Topic: Escalation -- O'Neill's Theorem and Vickrey Auctions
Reading: 6.1–6.6
Homework 7. Ch. 6: 3, 18, 23, 26 (due Friday, Nov 4 at 11:59pm)
Week of Oct 24 (Week 9):
Topic: More Social Choice—Social Welfare and May’s Theorem (Generalized), Arrow’s Impossibility Theorem
Reading: 7.1–7.4
MIDTERM EXAM -- in class on Wednesday, Oct 26. Covers Ch. 1-4
No calculators, electronic devices (cellphones, etc.) allowed. No notes or textbooks allowed.
Week of Oct 31 (Week 10):
Topic: The Gibbard-Satterthwaite Theorem and Single Peakedness
Reading: 7.5–7.6
Homework 8. Ch. 7: 1(a), 13, 17, 25, 26 (due Friday, Nov 11 at 11:59pm)
Week of Nov 7 (Week 11):
Topic: More Yes–No Voting—Magic Squares, Dimension Theory, and Vector-Weighted Voting Systems
Reading: 8.1–8.4
Homework 9. Ch. 8: 7, 8, 14, 17 (due Friday, Nov 18 at 11:59pm)
Week of Nov 14 (Week 12):
Topic: Johnston Power Index, Deegan-Packel Power Index, Ordinal Power (Incomparability)
Reading: 9.1–9.4
Homework 10. Ch. 9: 1, 2, 4 (due Friday, Nov 25 at 11:59pm)
Week of Nov 21 (Week 13):
Monday is reading day.
THANKSGIVING BREAK (Nov 23-25)
Week of Nov 28 (Week 14):
Topic: Ordinal Power (Comparability), A Theorem on Voting Blocks
Reading: 9.5-9.6
Homework 11. Ch. 9: 13, 14, 21, 25 (due Friday, Dec 9 at 11:59pm)
Week of Dec 5 (Week 15):
Topic: Models of Deterrence, Two-Person Zero-Sum Games
Reading: 10.1–10.4
Homework 12. Ch. 10: 5, 9, 10(a), 11 (due Wednesday, Dec 14 at 11:59pm)
Week of Dec 12 (Week 16):
Topic: Review. Wednesday is reading day.
FINAL EXAM -- Monday, Dec 19, 4:00pm. Meliora 224.