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A model of influence with an ordered set of possible actions

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  • Michel Grabisch

    ()

  • Agnieszka Rusinowska

    ()

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 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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File URL: http://hdl.handle.net/10.1007/s11238-009-9150-6
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Bibliographic Info

Article provided by Springer in its journal Theory and Decision.

Volume (Year): 69 (2010)
Issue (Month): 4 (October)
Pages: 635-656

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Handle: RePEc:kap:theord:v:69:y:2010:i:4:p:635-656

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

Related research

Keywords: Weighted positive influence index; Weighted negative influence index; Influence function; Follower of a coalition; Perfect follower; Kernel;

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References

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  1. René Van Den Brink & Agnieszka Rusinowska & Frank Steffen, 2009. "Measuring Power and Satisfaction in Societies with Opinion Leaders: Properties of the Qualified Majority Case," Post-Print halshs-00371813, HAL.
  2. Michel Grabisch & Agnieszka Rusinowska, 2008. "Influence functions, followers and command games," Documents de travail du Centre d'Economie de la Sorbonne, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne b08080, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  3. Hsiao Chih-Ru & Raghavan T. E. S., 1993. "Shapley Value for Multichoice Cooperative Games, I," Games and Economic Behavior, Elsevier, vol. 5(2), pages 240-256, April.
  4. Tchantcho, Bertrand & Lambo, Lawrence Diffo & Pongou, Roland & Engoulou, Bertrand Mbama, 2008. "Voters' power in voting games with abstention: Influence relation and ordinal equivalence of power theories," Games and Economic Behavior, Elsevier, vol. 64(1), pages 335-350, September.
  5. Harrie De Swart & Agnieszka Rusinowska, 2007. "On some properties of the Hoede-Bakker index," Post-Print halshs-00201414, HAL.
  6. Bolger, E M, 1986. "Power Indices for Multicandidate Voting Games," International Journal of Game Theory, Springer, Springer, vol. 15(3), pages 175-86.
  7. Michel Grabisch & Agnieszka Rusinowska, 2008. "Measuring influence in command games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00269084, HAL.
  8. Bolger, Edward M, 1993. "A Value for Games with n Players and r Alternatives," International Journal of Game Theory, Springer, Springer, vol. 22(4), pages 319-34.
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  12. Agnieszka Rusinowska, 2007. "The not-preference-based Hoede-Bakker index," Working Papers, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure 0704, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
  13. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence in a social network," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00308741, HAL.
  14. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 132-152, October.
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  16. M. Albizuri & José Zarzuelo, 2000. "Coalitional values for cooperative games withr alternatives," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 8(1), pages 1-30, June.
  17. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: controls," Games and Economic Behavior, Elsevier, vol. 45(1), pages 153-170, October.
  18. Dan S. Felsenthal & Moshé Machover, 2002. "Models and Reality: the Curios Case of the Absent Abstention," Homo Oeconomicus, Institute of SocioEconomics, vol. 19, pages 297-310.
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Citations

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Cited by:
  1. René van den Brink & Agnieszka Rusinowska & Frank Steffen, 2011. "Measuring Power and Satisfaction in Societies with Opinion Leaders: An Axiomatization," Documents de travail du Centre d'Economie de la Sorbonne, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne 11018, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  2. Grabisch, Michel & Rusinowska, Agnieszka, 2013. "A model of influence based on aggregation functions," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 316-330.
  3. Emmanuel Maruani & Michel Grabisch & Agnieszka Rusinowska, 2011. "A study of the dynamic of influence through differential equations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00587820, HAL.
  4. Grabisch, Michel & Rusinowska, Agnieszka, 2011. "A model of influence with a continuum of actions," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 576-587.
  5. Michel Grabisch & Agnieszka Rusinowska, 2010. "Iterating influence between players in a social network," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00543840, HAL.
  6. Agnieszka Rusinowska & Rudolf Berghammer & Harrie De Swart & Michel Grabisch, 2011. "Social networks: Prestige, centrality, and influence (Invited paper)," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00633859, HAL.
  7. Ren� van den Brink & Agnieszka Rusinowska & Frank Steffen, 2009. "Measuring Power And Satisfaction in Societies with Opinion Leaders: Dictator and Opinion Leader Properties," Tinbergen Institute Discussion Papers 09-052/1, Tinbergen Institute.

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