Uncertainty & Decisions: from individual to group choice

MoL Project: June 2011

Lecturer: Stéphane Airiau and Umberto Grandi

"The rational choice paradigm provides a way of thinking about the world, but it does not provide answers to a multitude of concrete questions. [...] Problems that range from the definition of probability to the meaning of happiness, from the notion of rationality to the essence of justice, belong to the realm of philosophy, but they pop up in practical guises in questions of the social sciences. [...] I believe the rational choice paradigm can be a powerful aid in thinking about such problems." -- Itzhak Gilboa

Aims: The aim of this project is to gain a solid comprehension of the standard theory of decision under uncertainty and of the main theorems of group decision making with complete information, and to explore their generalisations in uncertain domains.

• Learn the basics of individual decision under uncertainty
• Learn the basics of collective decision (with complete information)
• Explore the literature on collective decision theory under uncertainty

Format: The first half of the project will consist of lectures. In the last part, each student will give a presentation about an existing paper in the literature on group choice under uncertainty and will write a final paper on that topic. Topics of lectures will include:

• Background (environment without uncertainty)
  • Individual choice and preference, representation of utility
  • Group choices: Arrow's theore, Arrow-Debreu theorem
• Decision making under uncertainty
  • Objective uncertainty: von Neumann Morgenstern theorem
  • Subjective uncertainty: De Finetti and Savage's theorem
  • Condorcet Jury Theorem
  • Overview of group choices under uncertainty (which will be the topic for final papers)

• participation: 10%
• presentation: 30%
• final paper: 60%

• Notes on the theory of Choice. D. Kreps
• Rational choice. I. Gilboa
• Theory of decision under uncertainty. I. Gilboa
• An introduction to Decision Theory. M. Peterson
• Theory of Distributed Justice. J. Roemer
• Theory of value. G. Debreu
• A Primer in Social Choice Theory W. Gaertner

• June 1st: Introduction and representation
               Reading: Kreps Chapter 2 and Chapter 3, Peterson 5.1
• June 7th: von Neumann Morgenstern's theorem
               Reading: Peterson 5.2, Gilboa [TDUU] chapter 8
• June 9th: discussion about the proof of vNM's theorem from Peterson 5.2
• June 10th: De Finetti theorem
               Reading: Gilboa [TDUU] Chapter 9
• June 14th: Savage theorem
               Reading: Gilboa [TDUU] chapter 10, Kreps chapter 9
• June 15th: Arrow theorem
               Reading: Roemer chapter 1, Gaertner chapter 2
• June 17th:
  • Few papers about aggregation of preferences in presence of uncertainty
    
  • Critiques about Savage theorem
                 Reading:Gilboa [TDUU] Chapter 11 and 12, Gilboa [RD] chapter 1
• June 20th: Condorcet Jury theorem
               Reading: List and Goodin, Epistemic democracy: Generalizing the Condorcet Jury Theorem in Journal of Political Philosophy 2001.
• June 22nd: Arrow Debreu theorem
               Reading: (talk based on Debreu), Gilboa [RC] chapter 8
• June 24th: Presentations:
  • Pawel:
  • Bruno:

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Last modified: Mon May 16 12:51:00 CEST 2011