And Politics M110
Suggestions for topics for the Student Papers and
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):
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:
Title of the project
Names of students in the group
How will you divide the presentation: who will do what.
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.
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.
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?
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?
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!)
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.
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
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?
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!
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
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
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?
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
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
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
- 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