De Condorcet à Arrow via Guilbaud, Nakamura et les "jeux simples"

Abstract

The aim of this paper is to present Arrow's theorem and more generally the common framework of many results which can be called "Arrovian theorems". We begin by recalling the Condorcet majority rules and why they fail: the so called "effet Condorcet". These rules are examples of preference aggregation functions defined by a simple game, and then following Guilbaud's approach, we seek if in the class of all these functions we can find some functions avoiding this problem. The rather negative answer is given by the Guilbaud and Nakamura theorems. Taking then an axiomatic approach we show that some independent and Paretian preference aggregation functions avoiding the "effet Condorcet" are defined by a simple game. So the previous results allow to get several Arrovian theorems and finally Arrow's theorem. In the last section we give some historical and bibliographical comments on these results and on several developments showing essentially the robustness of Arrow's theorem.