This course will survey the use of probabilistic methods and computer simulations to study group decision making methods. The course will begin with an introduction to social choice theory (primarily focusing on the mathematical analysis of voting methods), with an emphasis on the use of probabilistic methods to study key issues in social choice theory. Additional topics include: the random utility model; calculating the probability of voting paradoxes (such as the Condorcet paradox); quantitative analysis of voting methods (e.g., finding the Condorcet efficiency and the Nitzan-Kelly index of a voting method); probabilistic voting methods (voting methods in which the output is a lottery over the set of alternatives); the impartial culture assumption (and related assumptions); and the Condorcet jury theorem and related results. Students will be have hands-on experience developing a computer simulation that will illustrate the main topics discussed in the course. Although previous programming experience will be helpful (especially with Python), the course will be accessible to students with no previous programming experience.
F. Brandl, F. Brandt, and C. Stricker. An analytical and experimental comparison of maximal lottery schemes, Social Choice and Welfare, 2021
F. Dietrich and K. Spiekermann, Jury Theorems, 2016
C. List and R. Goodin, Epistemic Democracy: Generalizing the Condorcet Jury Theorem, Journal of Political Philosophy, 2002.
M. Morreau, Democracy without Enlightenment: A Jury Theorem for Evaluative Voting, Journal of Political Philosophy, 2020.
M. Pivato, Voting rules as statistical estimators, Social Choice and Welfare, 40, 2013.