Mathématiques et sciences humaines. Mathematics and social sciences | |
Résolution de problèmes d'agrégation de préférences via l'approximation par des matrices bistochastiques | |
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
【 预 览 】
Files | Size | Format | View |
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RO201912020428663ZK.pdf | 512KB | download |