Midterm exam and final project

Midterm exam

• Your midterm will take place on Thursday, November 13, during class. 

• More details about what the exam will cover and how you should study for it can be found in this review sheet.

• Here are some review problems and their solutions.

• Here is the midterm exam, and here are the solutions. (Posted after the exam.)

Final project

For your final projects, you will write a 7-8 page paper on a topic of your choosing. The topic should broadly be about the interaction of mathematics and politics, and it may or may not be related to something we are studying in class. You should consult with me before you choose a topic. I will give you more details about the timeline for completing the paper in due time. Some potential topic options are

• • • Math and politics in your state

      • • How does your state vote? Does anything different happen on the local level? Are there attempts to change the voting method in your state? How are ties broken in your state? Is your state gerrymandered? Who runs the districting? Is there any math and politics education in your state's K-12 curriculum?

    • Ranked choice in practice

      • • How has ranked choice fared where it has been used (Maine, Alaska, various cities around the U.S.)? Is there evidence that it is producing "better" winners?

    • Primary elections

      • • Democratic and Republican primary elections are one of the main drivers of extreme political polarization and extremism. Examine how primaries are run and why they potentially produce candidates who are not representative of the party's voters. What are some alternatives to the usual primary elections, for example top-four open primaries? 

    • Strategic voting

      • • What are the ways in which voters can cast strategic votes beyond examples from class? What are some examples from real life? How big of a problem is strategic voting?

    • Proportional representation

      • • What is proportional representation? How does it work in other countries? Would it be possible to enact it in the U.S.? Would using multi-member districts with proportional representation decrease gerrymandering and provide opportunities for underrepresented groups? See this paper.

    • Measuring democracy

      • • How do we quantify the notion of a "good" or "bad" democracy? How do we measure representativeness and fairness? What are some democracy indicators and indices and how rigorous are they? 

    • Digital democracy

      • • New digital tools for enabling political participation, like sortition, citizen assemblies, participatory budgeting, liquid democracy.

    • Mathematics of polling

      • • How is it done, is it biased, what math is behind it?

    • Use of mathematical models in society

      • • How do math models and algorithms work? How are they biased? Look up the book Weapons of Math Destruction by Cathy O'Neil. Also see this New York Times article and this NPR article.

    • Mathematics of influencing voters on social media

      • • How do algorithms behind things like what Cambridge Analitica did work? Is there some cool math behind this? What is digital gerrymandering?

    • First Cryptography Wars of the 1990s

      • • Civil liberties vs. national security, clipper chip, PGP, backdoors, weakened encryption.

    • More on gerrymandering and mathematical ways of detecting and preventing it

      • • Probabilistic methods for detecting gerrymandering pioneered by MGGG and recent court cases using this.

    • Prison gerrymandering

      • • How the prison population is used as a gerrymandering tool in various states. See this article and this website.

    • More recent variants of power indices and calculations

      • • Some more sophisticated variants of the Banzhaf and Shapley-Shubik indices and some calculations of the power structure in current institutions like the European Parliament, the IMF, etc.

    • More on uses and misuses of statistics in politics

      • • Tools, examples, common pitfalls, etc.

    • Nash equilibrium

      • • History, proof, interesting examples in politics, how it fits in game theory.

    • Conflict and negotiation

      • • Game-theoretic approach to  modeling and understanding political conflict, war, negotiation, diplomacy, strategy, and cooperation.

    • Mechanism design

      • • Use the economic theory of mechanism design to start with certain desirable outcomes based on people's preferences and design a democracy that achieves them. 

    • Quantitative literacy and rational political thinking

      • • Is there a connection between the two?  Are people who are less numerate (quantitatively literate) less likely to think about politics rationally? This this webpage and this related article.

    • Political quantitative literacy education in K-12 in the U.S.

      • • Are any states including some math and politics education in their civics or math curriculum? Are topics like voting or apportionment taught anywhere in the K-12 system? What is the history of quantitative aspects of education in politics, civics, or history classes in the U.S.?

To help you with research for your project, LTS staff has also put together this helpful list of resources.