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A model of influence with an ordered set of possible actions

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Abstract

In the article, a yes–no model of influence is generalized to a multi-choice framework. We introduce and study the weighted influence indices of a coalition on a player in a social network where the players have an ordered set of possible actions. Each player has an inclination to choose one of the actions. Due to the mutual influence among players, the final decision of each player may be different from his original inclination. In a particular case, the decision of the player is closer to the inclination of the influencing coalition than his inclination was, i.e., the distance between the inclinations of the player and of the coalition is greater than the distance between the decision of the player and the inclination of the coalition in question. The weighted influence index which captures such a case is called the weighted positive influence index. We also consider the weighted negative influence index where the final decision of the player goes farther away from the inclination of the coalition. We consider several influence functions defined in the generalized model of influence and study their properties. The concept of a follower of a given coalition and its particular case, a perfect follower, are defined. The properties of the set of followers are analyzed.

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Authors and Affiliations

  1. Université Paris I Panthéon-Sorbonne, Centre d’Economie de la Sorbonne, 106-112 Bd de l’Hôpital, 75013, Paris, France

    Michel Grabisch

  2. GATE, CNRS UMR 5824, Université Lumière Lyon 2, 93, Chemin des Mouilles, B.P.167, 69131, Ecully Cedex, France

    Agnieszka Rusinowska

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  1. Michel Grabisch
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  2. Agnieszka Rusinowska
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Correspondence to Agnieszka Rusinowska.

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Grabisch, M., Rusinowska, A. A model of influence with an ordered set of possible actions. Theory Decis 69, 635–656 (2010). https://doi.org/10.1007/s11238-009-9150-6

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  • DOI: https://doi.org/10.1007/s11238-009-9150-6

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