2nd Semester 2019/20: Condorcet's Jury Theorem and Its Variations

Instructors

Adrian Haret

If you are interested in this project, please contact Adrian Haret by email.

Registration until 31 May 2020

ECTS

6

Description

The aim of this project will be to explore a cluster of theoretical results underpinning the concept of "the wisdom of crowds". The idea behind the wisdom of crowds phenomenon is that, through democratic decision processes such as voting, groups can be surprisingly effective at finding the truth. The cornerstone of this view is Condorcet's Jury Theorem: according to it there are certain conditions under which the majority can be shown, with mathematical rigour, to be virtually right on a yes-no question. Examples of this idea at work can be striking and unexpected.
Should we then delegate all our problems to the public? Are policy matters to be decided by majority vote? It all depends on how much stock we want put in theoretical results such as Condorcet's Jury Theorem, and during the course we will examine the matter on all sides. We will look at why the theorem holds, different ways in which it can fail, and where to go from there.
Work in this area falls within the scope of Computational Social Choice, Political Science and Philosophy.

Organisation

The first week (June 1-5) will consist of a series of presentations given by the instructors on the Condorcet Jury Theorem. We will go through the main argument, lay down the conditions under which it holds and see how robust the result is under some variations of these conditions. The students should then select a paper from the literature and give a short presentation on it during the second week (June 8-12). The idea here will be to get an overall idea of how the results of the Condorcet Jury Theorem (and, more generally, the group consensus) vary when the parameters of the model are varied. During the third week (June 15-19) the students will be encouraged to work on a research topic of their own, which will be documented and handed in during the fourth week (June 22-26).

Prerequisites

Some degree of mathematical maturity.

Assessment

The project is evaluated on a pass/fail scale. There will be (i) a few brief homework questions during the first week (not formally graded), (ii) the presentation during the second week, and (iii) 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.

References

 

[1] Marija Slavkovic. Condorcet’s jury theorem and the truth on the web. Vox Publica. March 15, 2017
https://voxpublica.no/2017/03/condorcets-jury-theorem-and-the-truth-on-the-web/

[2] Christian List. Social Choice Theory. In E. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Winter 2013 Edition), in particular Section 2.3
https://plato.stanford.edu/archives/win2013/entries/social-choice/

[3] Franz Dietrich, Kai Spiekermann. Jury Theorems. In M. Fricker (ed.), The Routledge Handbook of Social Epistemology. New York and Abingdon, 2020.
Online at https://philpapers.org/archive/DIEJT-4.pdf

More involved:

[4] Edith Elkind, 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
Online at https://www.cambridge.org/files/5015/1077/0783/9781107060432AR_final3.pdf