Résolution de problèmes d'agrégation de préférences via l'approximation par des matrices bistochastiques
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 c...
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| الحاوية / القاعدة: | URI:https://journals.openedition.org/msh, |
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| المؤلف الرئيسي: | |
| التنسيق: | Article ou chapitre numérique |
| اللغة: | Anglais |
| منشور في: |
Mathématiques et sciences humaines
2006
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| الموضوعات: | |
| الوصول للمادة أونلاين: | Accès Université d'Orléans et IFPM Accès Université d'Orléans et IFPM |
| الملخص: | 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. |
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