Le but de cet article est de procéder à une présentation pédagogique d'un concept étendu de rationalité, la rationalité stochastique. Dans une première partie, nous exposons le problème à l'aide d'un exemple simple et posons un ensemble de définitions préliminaires. Puis, dans une seconde partie, nous présentons le résultat fondamental de Falmagne (1978) s'appliquant aux situations de choix multiples ; l'approche ensembliste de cet auteur est formalisée à partir du concept de polynômes de Block-Marschak (1960). Dans une troisième partie, nous traitons du cas particulier des choix binaires, développant ainsi l'approche géométrique de Mac-Fadden-Richter (1970) reposant sur le concept de permutoèdre ; les applications potentielles de cette approche en théorie du vote, optimisation combinatoire et analyse des données ordinales sont brièvement évoquées. La dernière partie conclut.
The aim of this article is to undertake a pedagogical presentation of a wide-spread concept of rationality, the stochastic rationality. In a first part, we set the problem with the help of a simple example and we put a set of preliminary definitions. Then, in a second part, we expound the basic result of Falmagne (1978) applied to multiple choices situations ; the set approach of this author is formalized with the Block-Marshak (1960) polynomials. In a third part, we deal with the particular case of binary choices, expanding the geometrical approach of Mac-Fadden-Richter (1970) based on a permutation polytope ; the potentials applications of this approach in voting theory, combinatorial optimization and ordinal data analysis are briefly described. The last part concludes.
@article{MSH_1990__109__17_0,
author = {Bouyaux, Pascal},
title = {Pr\'ef\'erences et rationalit\'e stochastiques},
journal = {Math\'ematiques et Sciences humaines},
volume = {112},
year = {1990},
pages = {17-40},
mrnumber = {1053894},
zbl = {0708.90003},
language = {fr},
url = {http://dml.mathdoc.fr/item/MSH_1990__109__17_0}
}
Bouyaux, Pascal. Préférences et rationalité stochastiques. Mathématiques et Sciences humaines, Tome 112 (1990) pp. 17-40. http://gdmltest.u-ga.fr/item/MSH_1990__109__17_0/
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