2nd Semester 2021/22: # The Wisdom of Crowds: Jury Theorems, Information Cascades, and All That

Adrian Haret

The idea behind the wisdom of crowds is that groups can be smart! That is, individuals with different, and possibly wrong, beliefs can improve their chance of being correct about a ground truth state by aggregating their opinions. This is an exciting prospect, especially in today's atmosphere of anxiety about public opinion.

In this course we will try to understand situations in which wisdom of the crowds occurs, as well as ways in which it can break down. The material will be focused on a series of theoretical results that study conditions under which groups of agents can be reliable truth-trackers.

A cornerstone of the idea of the wisdom of crowds is the Condorcet Jury Theorem (CJT), and it is with it that we start. Its central message is that groups of agents can be perform well on a yes/no question, with larger groups performing better. However, the CJT turns out to be a fragile result, and many of its optimistic conclusions break down when the core assumptions are relaxed. We will thus try to see how group opinion can still be accurate even when agents exchange information, imitate and influence each other... and also how it can end up being spectacularly wrong.

Work in this area falls within the scope of Computational Social Choice, Political Science and Philosophy.


The first week will consist of a series of presentations given by the instructor on some selected topics (described above).

The students should then select a paper from the literature and give a short presentation on it during the second week.

During the third week the students will be encouraged to work on a research topic of their own (either alone or in a group), which will be documented and handed in during the fourth week.


Some knowledge of probability theory, some degree of mathematical maturity.


The project is evaluated on a pass/fail scale.

There will be:

  •  a few brief homework questions on the topics covered in the lectures (not formally graded);
  • the presentation of a paper of choice;
  • the final assignment.  

The final assignment is meant to be driven by the students' interests, and it can range from exploration of a novel research idea, to the analysis of one or more existing papers, or to the implementation of some experiments and simulations.

  1. Dietrich, Franz and Kai Spiekermann, "Jury Theorems", _The Stanford Encyclopedia of Philosophy_ (Summer 2022 Edition), Edward N. Zalta (ed.), forthcoming URL = <>.
  2. Easley, David and Jon Kleinberg. Networks, crowds, and markets. Cambridge University Press (2010), available at
  3. Elkind, Edith and Arkadii Slinko. Rationalizations of Voting Rules. In F. Brandt, V. Conitzer, U. Endriss, J. Lang, A. Procaccia (eds.), Handbook of Computational Social Choice, 2016: 169-196, available at

More references will be made available during the project.