Probabilistic Methods in Social Choice Theory

Instructor: Eric Pacuit (website)

ESSLLI 2021 • Online

August 9 - 13, 2021

16:00 - 17:30 CEST

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.

Day 1: Introduction to voting theory and voting paradoxes

August 9, 2021

E. Pacuit, Voting methods, Stanford Encyclopedia of Philosophy, 2019

B. Zwicker, Introduction to the theory of voting, In F. Brandt, V. Conitzer, U. Endriss, J. Lang, and A.D. Procaccia (eds.), Handbook of Computational Social Choice. Cambridge University Press, 2016.

Day 2: Simulating elections

August 10, 2021

Day 3: Quantitative analysis of voting methods

August 11, 2021

Day 4: Probabilistic voting methods

August 12, 2021

Day 5: Condorcet jury theorem and related results

August 13, 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.


github.com/epacuit/esslli2021