Résolution de problèmes d'agrégation de préférences via l'approximation par des matrices bistochastiques

Mathématiques et sciences humaines. Mathematics and social sciences

Takouda, Pawoumodom-L.¹ 

关键词: aggregation of preferences;    doubly stochastic matrices;    permutation matrice;    alternating projection;   

DOI  :  10.4000/msh.2881

学科分类：数学（综合）

来源: College de France * Ecole des Hautes Etudes en Sciences Sociales (E H E S S)

【 摘 要 】

In this work, we consider the classical problem of aggregation of preferences. We extend a previous work by Blin [5]. Under some assumptions, he formulated this problem as that of finding the nearest permutation matrix to a doubly stochastic matrix (called normalized of the agreement matrix, which collects the information contained in the expressed individual preferences). We reduce these assumptions, and we introduce a two-phase scheme for solving the problem. The first phase consists in approximating the matrix that contains the individual preferences information (which looses here the doubly stochastic character) by a doubly stochastic matrix using an algorithm proposed by the author [20 in a previous work. We thereby reduce the more general problem to that considered by Blin, which can be solved by using linear programming or, more directly, as a weighted bipartite matching problem.

【 授权许可】

Unknown