The paper concerns a dynamic model of influence in which agents make a yes-no decision. Each agent has an initial opinion which he may change during different phases of interaction, due to mutual influence among agents. We investigate a model of influence based on aggregation functions. Each agent modifies his opinion independently of the others, by aggregating the current opinion of all agents. Our framework covers numerous existing models of opinion formation, since we allow for arbitrary aggregation functions. We provide a general analysis of convergence in the aggregation model and find all terminal classes and states. We show that possible terminal classes to which the process of influence may converge are terminal states (the consensus states and non trivial states), cyclic terminal classes, and unions of Boolean lattices (called regular terminal classes). An agent is influential for another agent if the opinion of the first one matters for the latter. A generalization of influential agent to an irreducible coalition whose opinion matters for an agent is called influential coalition. The graph (hypergraph) of influence is a graphical representation of influential agents (coalitions). Based on properties of the hypergraphs of influence we obtain conditions for the existence of the different kinds of terminal classes. An important family of aggregation functions -- the family of symmetric decomposable models -- is discussed. Finally, based on the results of the paper, we analyze the manager network of Krackhardt.
A Model of Influence Based on Aggregation Function
Résumé
en
The paper concerns a dynamic model of influence in which agents make a yes-no decision. Each agent has an initial opinion which he may change during different phases of interaction, due to mutual influence among agents. We investigate a model of influence based on aggregation functions. Each agent modifies his opinion independently of the others, by aggregating the current opinion of all agents. Our framework covers numerous existing models of opinion formation, since we allow for arbitrary aggregation functions. We provide a general analysis of convergence in the aggregation model and find all terminal classes and states. We show that possible terminal classes to which the process of influence may converge are terminal states (the consensus states and non trivial states), cyclic terminal classes, and unions of Boolean lattices (called regular terminal classes). An agent is influential for another agent if the opinion of the first one matters for the latter. A generalization of influential agent to an irreducible coalition whose opinion matters for an agent is called influential coalition. The graph (hypergraph) of influence is a graphical representation of influential agents (coalitions). Based on properties of the hypergraphs of influence we obtain conditions for the existence of the different kinds of terminal classes. An important family of aggregation functions -- the family of symmetric decomposable models -- is discussed. Finally, based on the results of the paper, we analyze the manager network of Krackhardt.
Auteur(s)
Michel Grabisch1, 2
, Agnieszka Rusinowska1, 2
1
CES -
Centre d'économie de la Sorbonne
( 15080 )
- Maison des Sciences Économiques - 106-112 Boulevard de l'Hôpital - 75647 Paris Cedex 13
- France
Université Paris 1 Panthéon-Sorbonne UMR8174 ( 7550 )
;
Centre National de la Recherche Scientifique UMR8174 ( 441569 )
2
PSE -
Paris School of Economics
( 301309 )
- 48 boulevard Jourdan 75014 Paris
- France
Université Paris 1 Panthéon-Sorbonne ( 7550 )
;
École normale supérieure - Paris ( 59704 )
;
Université Paris Sciences et Lettres ( 564132 )
;
École des hautes études en sciences sociales ( 99539 )
;
École des Ponts ParisTech ( 301545 )
;
Centre National de la Recherche Scientifique ( 441569 )
;
Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement ( 577435 )
Date de publication
2013
Audience
Internationale
Nom de la revue
Mathematical Social Sciences
(ISSN : 0165-4896)
Publié par Elsevier
Revue non référencée dans Sherpa-Romeo
Page/Identifiant
316-330
Langue du document
Anglais
Comité de lecture
Oui
Vulgarisation
Non
Financement
Ce travail a bénéficié d'une aide de l'Etat gérée par l'Agence Nationale de la Recherche au titre du programme " Investissements d'avenir " portant la référence ANR-10-LABX-93-01. This work was supported by the French National Research Agency, through the program Investissements d'Avenir, ANR-10--LABX-93-01.
Domaine(s)
Sciences de l'Homme et Société/Economies et finances
D - Microeconomics/D.D8 - Information, Knowledge, and Uncertainty/D.D8.D85 - Network Formation and Analysis: Theory
D - Microeconomics/D.D8 - Information, Knowledge, and Uncertainty/D.D8.D83 - Search • Learning • Information and Knowledge • Communication • Belief • Unawareness
D - Microeconomics/D.D7 - Analysis of Collective Decision-Making/D.D7.D72 - Political Processes: Rent-Seeking, Lobbying, Elections, Legislatures, and Voting Behavior
C - Mathematical and Quantitative Methods/C.C7 - Game Theory and Bargaining Theory/C.C7.C73 - Stochastic and Dynamic Games • Evolutionary Games • Repeated Games
C - Mathematical and Quantitative Methods/C.C6 - Mathematical Methods • Programming Models • Mathematical and Simulation Modeling/C.C6.C65 - Miscellaneous Mathematical Tools
Michel Grabisch, Agnieszka Rusinowska. A Model of Influence Based on Aggregation Function. Mathematical Social Sciences, 2013, pp.316-330. ⟨halshs-00906367⟩