• Slides

• Places I have studied and worked at: Boston University, Brown University, University of Virginia, Louvain-la-Neuve University, MIT, University of Sarajevo

• Slides

Additional materials:

• A Mathematician's Apology (and the Wikipedia site).

• AMS Math Moments, with information on the many applications of math.

• What is topology?

• An example of how topology can be used in political science.

• An overview of topological data analysis. And another.

• Slides

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 on Kenneth Arrow.

• 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.

• Slides

Additional materials:

• Brief introduction to social choice theory.

• 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.

• Slides

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.

• Slides

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.

• You can read more about the 2016 elections here and here.

• 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.

• Slides

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.

• Apportionment and allocation of legislative seats

• Gerrymandering

• Cardinal (non-ranked) voting methods

• Cryptography and privacy

• Abstract math meets data science