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A model of influence in a social network

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Author Info
Michel Grabisch () (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I)
Agnieszka Rusinowska () (GATE - Groupe d'analyse et de théorie économique - CNRS : UMR5824 - Université Lumière - Lyon II - Ecole Normale Supérieure Lettres et Sciences Humaines)

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Abstract

In the paper, we study a model of influence in a social network. It is assumed that each player has an inclination to say YES or NO which, due to influence of other players, may be different from the decision of the player. The point of departure here is the concept of the Hoede-Bakker index - the notion which computes the overall decisional "power" of a player in a social network. The main drawback of the Hoede-Bakker index is that it hides the actual role of the influence function, analyzing only the final decision in terms of success and failure. In this paper, we separate the influence part from the group decision part, and focus on the description and analysis of the influence part. We propose among other descriptive tools a definition of a (weighted) influence index of a coalition upon an individual. Moreover, we consider different influence functions representative of commonly encountered situations. Finally, we propose a suitable definition of a modified decisional power.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00344457_v1.

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Date of creation: Nov 2008
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Handle: RePEc:hal:cesptp:halshs-00344457_v1

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Related research
Keywords: Influence function; influence index; decisional power; social network.;

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This paper has been announced in the following NEP Reports: References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Annick Laruelle & Federico Valenciano, 2005. "Assessing success and decisiveness in voting situations," Social Choice and Welfare, Springer, vol. 24(1), pages 171-197, January. [Downloadable!] (restricted)
  2. Gerard van der Laan & René van den Brink, 2002. "A Banzhaf share function for cooperative games in coalition structure," Theory and Decision, Springer, vol. 53(1), pages 61-86, August. [Downloadable!] (restricted)
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  3. (*), Gerard van der Laan & RenÊ van den Brink, 1998. "Axiomatizations of the normalized Banzhaf value and the Shapley value," Social Choice and Welfare, Springer, vol. 15(4), pages 567-582. [Downloadable!] (restricted)
  4. Vincent Merlin & Marc Feix & Dominique Lepelley & Jean-Louis Rouet, 2007. "On the Voting Power of an Alliance and the Subsequent Power of its Members," Post-Print halshs-00010168_v1, HAL. [Downloadable!]
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  5. René van den Brink & Peter Borm, 2002. "Digraph Competitions and Cooperative Games," Theory and Decision, Springer, vol. 53(4), pages 327-342, December. [Downloadable!] (restricted)
  6. René Brink & Peter Borm & Ruud Hendrickx & Guillermo Owen, 2008. "Characterizations of the β- and the Degree Network Power Measure," Theory and Decision, Springer, vol. 64(4), pages 519-536, June. [Downloadable!] (restricted)
  7. Moshé Machover & Dan S. Felsenthal, 2002. "Annexations and alliances: When are blocs advantageous a priori?," Social Choice and Welfare, Springer, vol. 19(2), pages 295-312. [Downloadable!] (restricted)
  8. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 132-152, October. [Downloadable!] (restricted)
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  1. Michel Grabisch & Agnieszka Rusinowska, 2009. "Measuring influence in command games," Social Choice and Welfare, Springer, vol. 33(2), pages 177-209, August. [Downloadable!] (restricted)
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