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A model of influence with an ordered set of possible actions

  • Agnieszka Rusinowska

    ()

    (Axe Economie mathématique et jeux - CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS)

  • Michel Grabisch

    ()

    (Axe Economie mathématique et jeux - CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS)

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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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number hal-00519413.

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Date of creation: 2010
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Handle: RePEc:hal:cesptp:hal-00519413
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  1. Edward M. Bolger, 2002. "Characterizations of two power indices for voting games with r alternatives," Social Choice and Welfare, Springer, vol. 19(4), pages 709-721.
  2. Michel Grabisch & Agnieszka Rusinowska, 2008. "Influence functions, followers and command games," Working Papers 0831, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
  3. 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.
  4. Agnieszka Rusinowska, 2007. "The not-preference-based Hoede-Bakker index," Working Papers 0704, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
  5. Bolger, Edward M, 1993. "A Value for Games with n Players and r Alternatives," International Journal of Game Theory, Springer, vol. 22(4), pages 319-34.
  6. 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.
  7. 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.
  8. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence in a social network," Theory and Decision, Springer, vol. 69(1), pages 69-96, July.
  9. Michel Grabisch & Agnieszka Rusinowska, 2009. "Measuring influence in command games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445126, HAL.
  10. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 132-152, October.
  11. 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.
  12. Edward M. Bolger, 2000. "A consistent value for games with n players and r alternatives," International Journal of Game Theory, Springer, vol. 29(1), pages 93-99.
  13. Harrie De Swart & Agnieszka Rusinowska, 2007. "On some properties of the Hoede-Bakker index," Post-Print halshs-00201414, HAL.
  14. M.J. Albizuri & J.C. Santos & J.M. Zarzuelo, 1999. "Solutions for cooperative games with r alternatives," Review of Economic Design, Springer, vol. 4(4), pages 345-356.
  15. MoshÊ Machover & Dan S. Felsenthal, 1997. "Ternary Voting Games," International Journal of Game Theory, Springer, vol. 26(3), pages 335-351.
  16. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: controls," Games and Economic Behavior, Elsevier, vol. 45(1), pages 153-170, October.
  17. Bolger, E M, 1986. "Power Indices for Multicandidate Voting Games," International Journal of Game Theory, Springer, vol. 15(3), pages 175-86.
  18. 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.
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