Week 1: A Mess of an Election
-
Reading — Preface and Chapter 1 Saari (feel free to just skim Sections 1.2 and 1.3).
Problems — None, but be prepared on Thu. 9/6 to discuss the reading assignment.
Week 2: What's So Good About Majority Rule?
-
Reading — Chapter 1 in Hodge and Klima.
Focus Problems — 6, 7, 13, 14, 21, 29.
Problems Due on Fri. 9/14 — 23, 26, 30, 31.
Week 3: Perot, Nader, and Other Inconveniences
-
Reading — Chapter 2 in Hodge and Klima.
Focus Problems — 5, 9, 10, 13, 16, 21.
Problems Due on Fri. 9/21 — 19, 23, 26, 33.
Week 4: Back into the Ring
-
Reading — Chapter 3 in Hodge and Klima.
Focus Problems — 6, 11, 13, 14, 15, 20.
Problems Due on Fri. 9/28 — 21, 25, 28, 29,
Week 5: Trouble in Democracy
-
Reading — Chapter 4 in Hodge and Klima.
Focus Problems — 5, 6, 7, 8, 14, 15, 25.
Problems Due on Tue. 10/9 — 17, 18, 31, 34 (a,b,c,e).
Week 6: Explaining the Impossible
-
Reading — Chapter 5 in Hodge and Klima.
Focus Problems — 2, 5, 7, 9, 12, 15, 19, 21, 22.
Problems Due on Fri. 10/12 — 17.
Note: You may work with up to three classmates, and your group need only submit one solution. Take some time to do a really good job with this assignment--you'll be happy you did so!
Week 7: One Person, One Vote?
-
Reading — Chapter 6 in Hodge and Klima.
Focus Problems — 14, 17, 22, 25, 27, 31.
Problems Due on Fri. 10/19 — 32, 33, 38, 39.
Week 8: Intro to Groups and Linear Algebra
-
Prepare for the midterm exam which will be an in-class exam on
Tuesday, October 30.
Week 9: Invariant Spaces
Week 10: Preferences, Procedures, and Chaos
-
Reading — Chapters 2-3 in Saari.
Problems Due on Fri. 11/9 — Find a profile for four candidates that...
-
(1) ...exhibits the behavior described in Theorem 2 (on p. 36).
(2) ...exhibits the behavior described in Theorem 3 (on p. 37).
(3) ...exhibits the behavior described in Theorem 4 (on p. 38).
(4) ...exhibits the behavior described in the second paragraph of p. 76.
Week 11: Strategic Voting
-
Reading — Chapter 4 in Saari.
Problems Due on Fri. 11/16 —
-
(1) For a three-candiate election, can you find a profile with a Condorcet loser who wins under at least one positional voting system?
(2) For a three-candidate election, can you find a profile with a Condorcet winner who does not win under any positional voting system?
(3) Andrew Hilger '13 recently told me the following:
"ASHMC has recently been looking into changing our voting system. Our current system is a two-round system requiring a majority to win, with a two-candidate runoff if necessary. Though this system mostly seems to work well, there have been a couple issues, mostly having to do with runoffs. Voter participation is always lower in runoffs, and having runoffs seems to contribute to voter fatigue, as evidenced by declining turnout in the recent back-to-back Freshman Class President and Honor Board elections."
If you would like your proposal to be shared with ASHMC, please also send it to me separately by email. Also, you may work with up to two of your classmates on the proposal. Make it a good one--it might actually be adopted!
Week 12: Creating Examples
-
Reading — Chapter 5 in Saari.
Problems — None. Enjoy Thanksgiving break!
Week 13: Other Procedures, Other Assumptions
-
Reading — By Thursday, please read Chapter 6 in Saari.
Problems — Begin zeroing in on a possible topic for your research project.
Week 14: Research Projects
-
Tuesday: Submit the first entry for your research journal.
Thursday: Submit the second entry for your research journal.
Details: First and foremost for now, please remember that your task is simply to explore something in voting theory that interests you. What is most important to me by far is that you spend some quality time working with your ideas.
If it's helpful to know, I think it's reasonable to plan on setting aside about four hours between each class meeting to work on your project. That includes reading, sketching, exploring, coding, etc., and it includes the time necessary to fill out your "journal" entry (on the form I gave you this morning).
I would appreciate it if your first journal entry explained what you are working on and why you chose it as a topic. I'd also appreciate seeing any conjectures, patterns, or results you were able to obtain over the weekend. In end, I'd like to be able to look at your journal entry and get the sense that you've been putting some time and energy into your project.
Remember that you'll bring your journal entry to class on Tuesday, and that I'll give you a chance to explain your ideas and progress to some of your classmates. On Tuesday, I'll also explain what we'll be doing the following week in terms of in-class presentations about your research projects.
Week 15: Research Presentations
-
Prepare and give a 2-3 minute presentation for your classmates about your research project. The schedule of presentations and other details will have been announced and discussed in class during the previous week.
Week 16: Finals Week
For half of your "final exam" in Math 189, you'll be writing two short essays. The prompts are below, and you may only use as sources your notes, our textbooks, and the research papers I have given you in class. Keep in mind that, as with most other exams, you may not discuss your answers with your classmates until all of the essays have been submitted. These essays are due on Thursday, Dec. 20, at 5:00 PM. Please slide them under my office door.
For these two short essays, as well as your final research project, please strive to create clear and compelling arguments, and to seek out and effectively use appropriate evidence. Finally, give some serious thought to the structure and flow of your essays and final research report, and remember to use these papers as vehicles to demonstrate your understanding of the ideas we have encountered.
FINAL EXAM
[10 points] Write a 500-750 word essay that addresses the following question: Why does Donald Saari prefer the Borda count to just about any other voting system?
[10 points] Write a 500-750 word essay that addresses the following question: What role does symmetry play when it comes to thinking about and understanding voting from a mathematical point of view?
[20 points] Write a 1000-1500 word essay that describes the goals, methods, and results of your research project.