Topic in discrete mathematics: Social Choice Theory.


Lecture notes: week I Much of the material in the first three lectures can be found in books on microeconomics. `Lecture notes in Microeconomic theory'' by Ariel Rubinstein contains the background material on individual preferences and choice (week I) as well as a chapter on Arrow theorem (week II) and expected utility theory (Problem set I).

Lecture notes (skeleton): week II Two proofs of Arrow's theorem were described: One following the presentation in Rubinstein's book and the other following the third proof in the article:

Three Brief Proofs of Arrow's Impossibility Theorem by John Geanakoplos.

Problem set I

Week III We defined social choice functions and proved the Gibbard-Satterthwaite theorem. We followed the presentation in

Arrow's Theorem and the Gibbard-Satterthwaite Theorem: A Unified Approach by Philip Reny

Week IV: The Shapley Shubik power index and information aggregation

We described the model of cooperative $n$ persons game and the Shapley value. We described the axiomatic definition of the value as well as the formulas of Shapley and of Owen. We stated the connection of Shapley-Shubik power index with information aggregation.

A good source is The Shapley Value by Eyal Winter.

The results on aggregation of information and on indeterminacy (next week) are from Social indeterminacy, by Gil Kalai.

Week V: Indeterminacy.