Topics in Research Methods
Global Studies Program
Center for Interdisciplinary Studies
University of Sarajevo
This is the page for a part of a graduate multi-instructor research methods course taught at at the Center for Interdisciplinary Studies of the University of Sarajevo in January 2021. The page contains slides from the lectures and accompanying materials. This part of the course was taught by Ismar Volić.
About the instructor
Places I have studied and worked at: Boston University, Brown University, University of Virginia, Louvain-la-Neuve University, MIT, University of Sarajevo
Research in mathematics
Additional materials:
A Mathematician's Apology (and the Wikipedia site).
AMS Math Moments, with information on the many applications of math.
An example of how topology can be used in political science.
An overview of topological data analysis. And another.
Mathematics of voting
Additional materials:
An excellent book on voting (without too much math).
Crazy example of vote splitting in a recent election in Massachusetts.
Crazy example of voting results in the UK.
More examples of vote splitting/spoiler effect. And here are some more.
A video introducing various voting methods and the Condorcet paradox.
Crazy/fun election facts from around the world. And some more. And some more.
Summary of ranked voting methods and where they are used.
An article about ethnic implications of instant runoff voting (talk about Bosnia-Herzegovina)
Video explaining the Arrow Impossibility Theorem and outlining its proof.
More formal treatment of the Arrow Impossibility Theorem.
Proof of the Impossibility Theorem.
Arrow's original paper on the Impossibility Theorem.
More on the Gibbart-Satterthwaite Theorem, and here is a proof.
Social choice theory
Additional materials:
Wikipedia entry on social choice theory with lots of good links.
Good introductory book on social choice theory and game theory.
An article discussing the implications of Arrow's Theorem on social choice theory.
Game theory
Additional materials:
An introductory video on game theory. And a video on game theory and U.S. politics.
One of the standard texbooks on game theory.
Wikipedia entry on game theory has good examples of real-life situation modeled by the Prisoner's Dilemma.
Biographies of John von Neumann, Oscar Morgenstern, and John Nash.
More on the fair division problem from the Talmud.
More on solving the bankruptcy problem.
U.S. Electoral College
Additional materials:
More details about the Electoral College.
A video explaining the Electoral College.
Article on the history of the Electoral College and some ways to fix it.
Here is a site that encodes the difference between the popular votes and the electoral college votes for presidential elections since 1972.
Under very reasonable assumptions, all you need is 23% of the popular vote to win the Electoral College! Here is how.
Quantification of power
Additional materials:
More on John Banzhaf, with links to materials on the Banzhaf power index.
Calculator that computes the Banzhaf power index of any weighted voting system.
More on the Shapley-Shubik power index. And here is another document that explains it and works out some examples.
Calculating the power distribution in the UN Security Council.
Calculating the power distribution in the IMF.
Other things we would talk about if we had infinite time
Apportionment and allocation of legislative seats
Gerrymandering
Cardinal (non-ranked) voting methods
Cryptography and privacy
Abstract math meets data science