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A model of influence in a social network

Author

Listed:
  • Michel Grabisch

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Agnieszka Rusinowska

    (GATE - Groupe d'analyse et de théorie économique - UL2 - Université Lumière - Lyon 2 - ENS LSH - Ecole Normale Supérieure Lettres et Sciences Humaines - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Michel Grabisch & Agnieszka Rusinowska, 2008. "A model of influence in a social network," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00344457, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00344457
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00344457
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    References listed on IDEAS

    as
    1. Michel Grabisch & Fabien Lange, 2007. "Games on lattices, multichoice games and the shapley value: a new approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(1), pages 153-167, February.
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    4. Agnieszka Rusinowska, 2007. "The not-preference-based Hoede-Bakker index," Working Papers 0704, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    5. Agnieszka Rusinowska, 2007. "The not-preference-based Hoede-Bakker index," Post-Print halshs-00142482, HAL.
    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.
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    8. Agnieszka Rusinowska, 2007. "The not-preference-based Hoede-Bakker index," Post-Print halshs-00142482, HAL.
    9. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
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    11. R J Johnston, 1978. "On the Measurement of Power: Some Reactions to Laver," Environment and Planning A, , vol. 10(8), pages 907-914, August.
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    13. 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.
    14. Moshé Machover & Dan S. Felsenthal, 2002. "Annexations and alliances: When are blocs advantageous a priori?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(2), pages 295-312.
    15. (*), Gerard van der Laan & RenÊ van den Brink, 1998. "Axiomatizations of the normalized Banzhaf value and the Shapley value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(4), pages 567-582.
    16. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 132-152, October.
    17. 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.
    18. Pradeep Dubey & Lloyd S. Shapley, 1979. "Mathematical Properties of the Banzhaf Power Index," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 99-131, May.
    19. Rae, Douglas W., 1969. "Decision-Rules and Individual Values in Constitutional Choice," American Political Science Review, Cambridge University Press, vol. 63(1), pages 40-56, March.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Förster, Manuel & Grabisch, Michel & Rusinowska, Agnieszka, 2013. "Anonymous social influence," Games and Economic Behavior, Elsevier, vol. 82(C), pages 621-635.
    2. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence with an ordered set of possible actions," Theory and Decision, Springer, vol. 69(4), pages 635-656, October.
    3. Michel Grabisch & Agnieszka Rusinowska, 2009. "Measuring influence in command games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 177-209, August.
    4. Grabisch, Michel & Rusinowska, Agnieszka, 2013. "A model of influence based on aggregation functions," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 316-330.
    5. Grabisch, Michel & Rusinowska, Agnieszka, 2011. "Influence functions, followers and command games," Games and Economic Behavior, Elsevier, vol. 72(1), pages 123-138, May.
    6. Berghammer, Rudolf & Rusinowska, Agnieszka & de Swart, Harrie, 2013. "Computing tournament solutions using relation algebra and RelView," European Journal of Operational Research, Elsevier, vol. 226(3), pages 636-645.
    7. Grabisch, Michel & Poindron, Alexis & Rusinowska, Agnieszka, 2019. "A model of anonymous influence with anti-conformist agents," Journal of Economic Dynamics and Control, Elsevier, vol. 109(C).
    8. Robin, Stéphane & Rusinowska, Agnieszka & Villeval, Marie Claire, 2014. "Ingratiation: Experimental evidence," European Economic Review, Elsevier, vol. 66(C), pages 16-38.
    9. Buechel, Berno & Hellmann, Tim & Klößner, Stefan, 2015. "Opinion dynamics and wisdom under conformity," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 240-257.
    10. Emmanuel Maruani & Michel Grabisch & Agnieszka Rusinowska, 2011. "A study of the dynamic of influence through differential equations," Documents de travail du Centre d'Economie de la Sorbonne 11022, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    11. Ushchev, Philip & Zenou, Yves, 2020. "Social norms in networks," Journal of Economic Theory, Elsevier, vol. 185(C).
    12. 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.
    13. 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.
    14. Massimo Riccaboni & Anna Romiti & Gianna Giudicati, 2011. "Co-experience Network Dynamics: Lessons from the Dance Floor," DISA Working Papers 2011/02, Department of Computer and Management Sciences, University of Trento, Italy, revised 28 Mar 2011.
    15. Berghammer, Rudolf & Rusinowska, Agnieszka & de Swart, Harrie, 2010. "Applying relation algebra and RelView to measures in a social network," European Journal of Operational Research, Elsevier, vol. 202(1), pages 182-195, April.
    16. Michel Grabisch & Agnieszka Rusinowska, 2010. "Iterating influence between players in a social network," Documents de travail du Centre d'Economie de la Sorbonne 10089, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    17. repec:hal:pseose:halshs-00906367 is not listed on IDEAS
    18. repec:hal:pseose:hal-00756696 is not listed on IDEAS

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    More about this item

    Keywords

    social network; Influence function; influence index; decisional power; social network.; Fonction d'influence; indice d'influence; pouvoir décisionel; réseau social.;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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