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A model of influence in a social network

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  • Michel Grabisch

    ()

  • Agnieszka Rusinowska

    ()

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.

(This abstract was borrowed from another version of this item.)

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Bibliographic Info

Article provided by Springer in its journal Theory and Decision.

Volume (Year): 69 (2010)
Issue (Month): 1 (July)
Pages: 69-96

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Handle: RePEc:kap:theord:v:69:y:2010:i:1:p:69-96

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Web page: http://www.springerlink.com/link.asp?id=100341

Related research

Keywords: Influence function; Influence index; Decisional power; Social network; C7; D7;

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References

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  1. 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.
  2. Herings, P.J.J. & Laan, G. van der & Talman, A.J.J., 2000. "Cooperative Games in Graph Structure," Discussion Paper 2000-90, Tilburg University, Center for Economic Research.
  3. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 132-152, October.
  4. Michel Grabisch & Fabien Lange, 2007. "Games on lattices, multichoice games and the shapley value: a new approach," Computational Statistics, Springer, vol. 65(1), pages 153-167, February.
  5. Agnieszka Rusinowska, 2007. "The not-preference-based Hoede-Bakker index," Post-Print halshs-00142482, HAL.
  6. Dan Felsenthal & Moshé Machover & William Zwicker, 1998. "The Bicameral Postulates and Indices of a Priori Voting Power," Theory and Decision, Springer, vol. 44(1), pages 83-116, January.
  7. (*), 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.
  8. René van den Brink & Peter Borm, 2002. "Digraph Competitions and Cooperative Games," Theory and Decision, Springer, vol. 53(4), pages 327-342, December.
  9. 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, HAL.
  10. Annick Laruelle & Federico Valenciano, 2005. "Assessing success and decisiveness in voting situations," Social Choice and Welfare, Springer, vol. 24(1), pages 171-197, January.
  11. R J Johnston, 1978. "On the measurement of power: some reactions to Laver," Environment and Planning A, Pion Ltd, London, vol. 10(8), pages 907-914, August.
  12. Gerard van der Laan & René van den Brink, 1998. "Axiomatization of a class of share functions for n-person games," Theory and Decision, Springer, vol. 44(2), pages 117-148, April.
  13. 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.
  14. Dan S. Felsenthal & Moshé Machover, 2002. "Annexations and alliances: When are blocs advantageous a priori?," Social Choice and Welfare, Springer, vol. 19(2), pages 295-312, April.
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