A model of influence with an ordered set of possible actions |
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Authors: | Michel Grabisch Agnieszka Rusinowska |
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Institution: | (1) Department of Economics, Brown University, 64 Waterman Street, Providence, RI 02912, USA;(2) Department of Mathematics, Advanced Teachers’ Training College, University of Yaounde 1, P.O. Box 47, Yaounde, Cameroon |
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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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