Mathematics And Politics M110

Suggestions for topics for the Student Papers and Presentations:

Remember, regardless whether you take a more mathematical project or an essay, it is important to not just rehash things you found, but to submit a serious effort on your part. Look up (and list at the end of the paper) several relevant references. Document your arguments with examples from those references, wherever relevant. When possible, try to be quantitative. I want to see something that is related to the material covered in class, but that was not actually covered in the class.

I place a premium on your figuring out things, rather than reporting hearsay. Or if you do report on what you found in the references, make sure that you explain clearly what is going on - even if this means going in greater detail than in your references. If there are some conclusions to be drawn, give them! Give the references that you used.

Let me remind you about grading policy (I talked about this in class):

Homework: 25%

Four Tests: 50%

Student Projects: 25% (written part, participation and presentation)

Student projects consist of written assignment, and a presentation. You can work in groups (but don’t have to) of up to three (3) people. If your project is a group project, the first page has to list the following:

1. Title of the project

2. Names of students in the group

3. How will you divide the presentation: who will do what.

4. Who did what fraction of the work. If somebody did not participate – I want to know.

Each student in a group: on a separate sheet of paper, write a one-paragraph (handwritten) summary of the paper, and indicate for every other member of your group the magnitude of her/his contribution. This is to be turned in separately.

The absolute deadline for handing in the final version of the papers is Tuesday, Nov 21. Student presentations will be held during the last two weeks of the classes, after the Thanksgiving break.

POSSIBLE TOPICS: this is not an exhaustive list - you can come up with your own topic, but you must clear it with me first.

• CHAPTER 11: Approval Voting. Is it better, worse, or just different from the other voting systems we discussed in class. Find out more about it. Describe the effectiveness of this voting procedure in several real-life (or hypothetical) examples. Make a conclusion (and support it) about the usefulness of this voting method.
  
  
• CHAPTER 11: Kenneth J. Arrow and Arrow’s impossibility theorem. Why is he important? What did he do? Explain in your own words the (complete) proof of the Arrow’s impossibility theorem. What is the significance of this theorem? What does it mean in practical terms?
  
  
• CHAPTER 8 and 11: Choose an issue of current interest. Prepare a short (at most 5-6 questions) questionnaire to determine opinions on this issue. Choose a sample of about 25-50 students, administer your questionnaire, and describe the results. Use the techniques of Chapter 11 to determine the winning opinion (option) using different voting strategies. Also, describe your experiences in designing and carrying out the survey. At the end, ask yourselves whether the questions could have been phrased in a better way. Is your sample really random?
  
  
• CHAPTER 8: The statistics section gives a discussion of "lying" with visualization of data. Find at least 6 different instances of such misleading visual representation of data in the newspapers or news magazines of the last few months, and explain why they are misleading, and how you would have made a visual representation to make the same point, but in an honest way. (Only serious papers please---no tabloids!)
  
  
• CHAPTER 8: Spotlight 8.1 in "For all Practical Purposes" explains “How the Poll Was Taken”. Investigate how other companies, in particular Gallup, conduct polls, and why is it so complicated? Describe the historical blunder of Literary Digest in 1936. Explain in detail how a possible bias can be introduced in a poll.
  
  
• CHAPTER 8: Control Charts. What is a control chart? How to build a control chart using hand calculator. Relationship between control charts and uncertainty. Example of application of control charts
  
  For Chapter 12 projects: Check out the following web page: http://fourier.math.temple.edu/cgi-bin/manager
  
  
• CHAPTER 12: Spotlight 12.3 in "For all Practical Purposes" explains about a Supreme Court case where power indices were discussed. Find more material about this case and prepare a report on it; explain the points of view of the different parties, and how using power indices differs from standard proportional representation. What is your opinion?
  
  
• CHAPTER 12: In class we (will) learn about the Banzhaff power index and the Shapley-Shubik power index (from p.279 on). Both the Banzhaff and the Shapley-Shubik power indices are also explained (as well as two other power indices) in the book "Mathematics and Politics" by Alan Taylor (from p. 211 on; the book is on reserve in the Library); Taylor's book explains better how you compute the indices for systems too large to do by eye-balling. Compute both the Banzhaff and the Shapley-Shubik indices for a mini-system with a President, a House and a Senate, in which the Senate and the House both have only 6 members. Assume also that a measure passes if at least half the House and half the Senate approve, and if the President agrees, or if 2/3 of both House and Senate approve, regardless of what the President thinks. What is the power index of the Presidents, of a Senator, or of a Representative in both systems? Taylor's book also gives both power indices for the US Federal system. Which do you think reflects reality best? Motivate your answer!
  
  
• CHAPTER 12: Investigation of other systems of government. This question is concerned with an analysis of the system of government and electoral system of a foreign country. Choose a foreign country from the list of web sites on National Parliaments (http://www.polisci.umn.edu/information/parliaments/index.html) of foreign governments is available from the Department of Political Science at the University of Minnesota.
  A complete investigation of the topic should include but not be limited to answers to the following questions. Your bibliography should not be limited to the web site for the country's parliament.

· What is the structure of the government?

· What is the size of the parliament? What voting methods are used to elect members of the parliament? Are these local elections, that is does each member represent a particular geographic district, or are they at-large nationwide elections? Are the elections for particular individuals or do you vote for a party? If the elections are nationwide, how is representation determined, for example, is there a quota for a minimum number of votes in order to seat a member of parliament, how does the number of representatives assigned to a party relate to the percentage of vote that party received?

· How is the rest of the government determined? Does the parliament determine the chief executive (for example the prime minister) or is there a separate election for the chief executive? How are other ministers of state selected?

· Consider the distribution of seats in the current parliament. Use the computer web site we used in class to compute the power of each of the parties. If possible, consider previous parliaments. How has the power distribution changed?

· Are there any current issues being discussed in the country about the procedures used or the structure of the government? Have there been any recent changes adopted or proposed?

· What is your overall sense of the system? What are its strengths and weaknesses?

• CHAPTER 12: Alternate methods used in state and local voting in the United States. Most of the elections in the United States are determined by plurality voting and most representation in the United States is by single-member geographic districts. There are, however, exceptions. In this paper you should investigate these exceptions. Some information about different voting procedures being used in this country is available at the following site maintained by the Center for Voting and Democracy (http://www.fairvote.org/), Takoma Park, MD:
  The questions to answer should include but not be limited to:

· Where in the US are other voting systems--cumulative voting, single transferable votes or approval voting--being used in determining elections? Carefully describe how each of these systems is being implemented.

· How did these alternate systems develop? How long have they been in use? Were there particular fairness issues that they were designed to address?

· Are there places, which have recently proposed alternate systems? What rationale was given for the proposed change? Were these changes accepted or defeated? Why?

· More generally, under what circumstances do you think voting systems other than plurality voting should be considered? Why?

• CHAPTER 12: European Union In class we mentioned European Union as an example of weighted voting system. This question is concerned with a further examination of the structure of the European Union, the distribution of power and the proposals for the expansion of the EU.
  A complete investigation of the topic should include but not be limited to answers to the following questions.
• What is the current membership of the European Union? How has that membership changed since its formation? What changes are proposed in the future?
• How does governance work in the European Union? What is the relationship between the Council of Ministers and the European Parliament? What are the rules for decision making in each body? How many votes are required for passage of any measure? Is there a committee structure which works to develop proposals which are then voted on by the entire membership? Are there other ways that proposals are placed before the membership?
• If we focus on the Council of Ministers, how is power currently distributed in the EU? How does that compare to the power distribution of the past or the projected power distribution in the future? Are there agreed upon principles about how votes and power should be distributed?
• What are the issues surrounding the expansion of the EU? Are there competing proposals about how to distribute votes in the Council of Ministers in an expanded EU? How does the power distribution compare in each of these proposals? Do these proposals seem to be in keeping with any agreed upon principles for the union?
  
  
• CHAPTER 15: Tennis. In tennis, one player often prefers to play from the baseline while her opponent prefers a serve-and-volley game (i.e., likes to come to the net). The baseline player attempts to hit passing shots. This player has a choice of hitting “down the line” or “crosscourt”. The net player must often guess correctly which direction the ball will go in order to cover the shot. Formulate this situation as a duel game and discuss appropriate strategies for the players. Make some assumptions about the winning percentages of different kinds of shots for a particular tennis player, and determine the nest strategy for his/her opponent,
  
  
• CHAPTER 15: Iterated prisoner’s dilemma. Investigate why is prisoner’s dilemma so intriguing. Start with The Prisoner's Dilemma page on the internet http://www.xs4all.nl/~helfrich/prisoner/, and continue from there. Address the example of spatial iterated prisoner’s dilemma. At least one of the references must be a print edition.