Sci199Y --- Strategy, Voting, Power and Proof

Professor: Mary Pugh, mpugh@math. utoronto.ca
Office hours: by appointment. Please email.
Office location: room 3141, Earth Sciences Centre, 22 Russell Street

If you're going to send me email, please include "sci199" in the subject line. Otherwise, there's a good chance my spam filter will filter your email.

The textbook is "Mathematics and politics: strategy, voting, power and proof" by Alan Taylor. You should buy the book from the campus bookstore. It should be relatively cheap. If you can't afford it, you can buy a used copy from abebooks.com. Also, there are two copies at Robarts and one at the Math library. The call number is JA77.T39 1995X .

It's three in the morning. How can you find that journal article you need?
In this course, you may find yourself wanting to look up articles that are referred to by the book. For example, the chapter on the dollar auction refers to a 1971 article by Martin Shubik and a 1986 article by Barry O'Neill. These are interesting articles --- you should read over the introductions and conclusions, if you have time. Note: if you're not UofT affiliated (and hence wouldn't have access to this article through our e-resources) then you are violating copyright law if you look at these articles.
How did I find these articles? (How should you find these articles when you need to?) First, I made sure that I could access the university's resources even though I was at home. When I'm at home, I look like some random person with a sympatico account and I had to do something to inform the University system that I have a right to look at University resources. How did I do this? Go to the Library's web-page on my.access and learn how. Note: if you're at a dorm computer it may be that you're automatically trusted, so before going too far, try to access the university's resources and try my.access only if you fail.
Now that you have access to the university's resources, go to the library's main web-page. On the left, you'll see a link for e-Resources. Click on it. Now, click on e-Journals & Preprints. If you're looking for Shubik's article, you know you're looking for an article in the Journal of Conflict Resolution. So type "conflict resolution" in the search window. You see the journal and click on its title. Now you go to "search this journal". If you search on Shubik as the author, you'll find seven articles, one of which is the one you're looking for. You can now view and print the article! Welcome to the glorious world of research! You have access to a wealth of information via these electronic resources. Use them happily and plentifully. But remember that if you let your friends or family use them, then you're stealing just as much as if you were to steal cable or towels from a hotel. These resources cost the UofT lots of money and are provided for people affiliated with the UofT.

Voting

How should we vote? Here's a recent article from the New York Times about different voting schemes. Note: if you're not UofT affiliated (and hence wouldn't have access to this article through our e-resources) then you are violating copyright law if you look at this article.
Woes in the European Union
What's the big deal? What was agreed upon in Nice? What's the "double majority" they refer to? "A double majority means that decisions must be approved by at least 50 percent of the member countries and that these countries must represent at least 60 percent of the EU population. Poland and Spain have voiced their opposition to the planned double majority voting system. They would like to retain the voting system agreed on in Nice under which they each have nearly as many votes as Germany even though their populations are only about half as large."
Bloc-like voting in the US. Here's a really cool website that Hibo found. It considers large-scale voting patterns in the US.
A quick way to compute power indices Here's a sweet website that Byoung Jun found. It computes four power indices for you.
Proportional Voting in Canada Here's a Globe and Mail article which describes a recent report on electoral reform in Canada. And here's the Law Commission of Canada report it's describing. Here's a column by a UofT law professor about proportional voting versus "first past the post" voting.

Game Theory

Good News, Everybody! Game theory is everywhere! Check out all these places where it shows up. It even shows up in South Park. Some of the links are out of date but since they provide bibliographic references and since you're at a university, you can probably track down whatever you want...
S.J. Brams has written a wide variety of books where he applied game theory methods in different arenas. Have a look at this list of books and see if any intrigue you. And then go to the library!
Today's the Superbowl... Here's a New York Times article about game theory analysis of strategy in football. (Note: if you're not UofT affiliated, and hence wouldn't have access to this article through our e-resources, then you are violating copyright law if you look at this article. ) And here's the article by David Romer being referred to.
Some political applications of Game Theory to Radical Religious Militias, to language-learning among immigrants, to environmental regulation, to Ultra-Orthodox Jews.
the Yom Kippur War Our book has a short overview of the Yom Kippur War. Here are some additional readings. Read them with a grain of salt. Here's what the Federation of American Scientists has to say. Here's a long and in no way unbiased article by a former member of the Knesset. Here are some summaries: one , two , and three. Here's a really nice timeline. And finally, here are two things that every educated person should know about: detente and cold war.
Rock, Paper, Scissors Need some practice? Here's a computer you can play against. Also, here's the World Rock Paper Scissors Society. Here's a New York Times story about competing in a Rock Paper Scissors competition. And Here's one about two auction houses playing Rock Paper Scissors to see who'll win the rights to auction off a multi-million dollar art collection. (Note: if you're not UofT affiliated, and hence wouldn't have access to this article through our e-resources, then you are violating copyright law if you look at this article. )

Auctions

A short and somewhat vague article on one approach to auctions. Here's information on four types of auctions. And here's a New York Times article about an interesting way to do well bidding on EBay... Note: if you're not UofT affiliated (and hence wouldn't have access to this article through our e-resources) then you are violating copyright law if you look at this article.
Vickrey's 1961 article Here's the origin of the Vickrey Auction. Of course, Mr Vickrey didn't call it that himself. :-) Note: if you're not UofT affiliated (and hence wouldn't have access to this article through our e-resources) then you are violating copyright law if you look at this article.
Dutch Auctions in the News Here's a recent New York Times article about the Aalsmeer flower auction in the Netherlands. Make sure to go visit it when you're in Amsterdam! Note: if you're not UofT affiliated (and hence wouldn't have access to this article through our e-resources) then you are violating copyright law if you look at this article.

Hey Ya!

Mathematics in the "real world" Here is a collection of columns by Ivar Peterson. They're very readable and may give you some ideas to follow. What is "behavioral economics"? Here is a New York Times article about it. Note: if you're not UofT affiliated (and hence wouldn't have access to this article through our e-resources) then you are violating copyright law if you look at this article.

Tips on Writing Research Articles Check out the following page. In the middle of the second paragraph is a linke to "logical structure". Look here for a good skeleton. Pay attention to the left of the two columns --- introduction, methodology, results, and conclusions & discussions. The right column isn't quite so relevant; it has to do w/ the wrapping of the entire thing. For my satisfaction, you would do:
title
author
left column of stuff from the "logical structure" page
references
appendices
If you were submitting the article to a journal, you'd have to do more of the stuff in the right column. Also, on the left of the webpage there are links to various things. Of especial use are "RULES FOR RA SECTIONS" and "MORE LINKS".


Welcome to University! Here are some tips.
  • Exercise and eat properly. Make sure to get at least seven hours of sleep a night.
  • Find some study buddies. Talk to your classmates --- they're here to help you and you them.
  • My friend Mark has some very good study tips for Calculus. His advice holds for pretty much all classes.
  • If test-taking generally makes you nervous, have a look at the test-taking brochure from the University of Illinois at Urbana-Champaign. They also have brochures on other aspects of student life --- have a look --- they're soundly written. For something more than brochures, the University of Toronto has a counselling and learning skills centre.