A model of influence with an ordered set of possible actions. Theory and Decision

Abstract. In the paper, a yes-no model of influence is generalized to a multi-choice framework. We introduce and study weighted influence indices of a coalition on a player in a social network, where players have an ordered set of possible actions. Each player has an inclination to choose one of the actions. Due to influence of a coalition of other players, a final decision of the 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., a distance between the inclinations of the player and of the coalition is greater than a 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 further 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. JEL Classification: C7, D