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A model of influence based on aggregation functions

Author

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  • Michel Grabisch

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Agnieszka Rusinowska

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract
The paper concerns a dynamic model of influence in which agents have to make a yes-no decision. Each agent has an initial opinion, which he may change during different phases of interaction, due to mutual influence among agents. The influence mechanism is assumed to be stochastic and to follow a Markov chain. In the paper, we investigate a model of influence based on aggregation functions. Each agent modifies his opinion independently of the others, by aggregating the current opinion of all agents, possibly including himself. We provide a general analysis of convergence in the aggregation model and give more practical conditions based on influential players. We show that the process of influence converges always to one of the two consensus states, and there may exist other terminal classes, which are either cyclic or union of Boolean lattices. We give sufficient conditions for avoiding these additional terminal classes, based on properties of the graph of influence and influential players. We also introduce the notion of influential coalition and show that it can fully describe terminal classes. Some important families of aggregation functions are discussed.

Suggested Citation

  • Michel Grabisch & Agnieszka Rusinowska, 2011. "A model of influence based on aggregation functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00639677, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00639677
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00639677
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    References listed on IDEAS

    as
    1. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence in a social network," Theory and Decision, Springer, vol. 69(1), pages 69-96, July.
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    4. 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.
    5. 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.
    6. Grabisch, Michel & Rusinowska, Agnieszka, 2011. "Influence functions, followers and command games," Games and Economic Behavior, Elsevier, vol. 72(1), pages 123-138, May.
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    16. Peter M. DeMarzo & Dimitri Vayanos & Jeffrey Zwiebel, 2003. "Persuasion Bias, Social Influence, and Unidimensional Opinions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 118(3), pages 909-968.
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    21. Bogaçhan Çelen & Shachar Kariv, 2004. "Distinguishing Informational Cascades from Herd Behavior in the Laboratory," American Economic Review, American Economic Association, vol. 94(3), pages 484-498, June.
    22. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2009. "Aggregation functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445120, HAL.
    23. Pan, Zhengzheng, 2010. "Trust, influence, and convergence of behavior in social networks," Mathematical Social Sciences, Elsevier, vol. 60(1), pages 69-78, July.
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    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Michel Grabisch & Agnieszka Rusinowska, 2020. "A Survey on Nonstrategic Models of Opinion Dynamics," Games, MDPI, vol. 11(4), pages 1-29, December.
    2. Förster, Manuel & Grabisch, Michel & Rusinowska, Agnieszka, 2013. "Anonymous social influence," Games and Economic Behavior, Elsevier, vol. 82(C), pages 621-635.
    3. Ulrich Faigle & Michel Grabisch, 2017. "Game Theoretic Interaction and Decision: A Quantum Analysis," Games, MDPI, vol. 8(4), pages 1-25, November.
    4. 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).
    5. Alexis Poindron, 2019. "A general model of synchronous updating with binary opinions," Documents de travail du Centre d'Economie de la Sorbonne 19024, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    6. Alexis Poindron, 2019. "A general model of synchronous updating with binary opinions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02372486, HAL.
    7. Rusinowska, Agnieszka & Taalaibekova, Akylai, 2019. "Opinion formation and targeting when persuaders have extreme and centrist opinions," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 9-27.
    8. GRABISCH, Michel & RUSINOWSKA, Agnieszka & VENEL, Xavier, 2022. "Diffusion in large networks," Journal of Economic Dynamics and Control, Elsevier, vol. 139(C).
    9. Michel Grabisch & Agnieszka Rusinowska & Xavier Venel, 2022. "Diffusion in large networks," Post-Print halshs-03688783, HAL.
    10. Poindron, Alexis, 2021. "A general model of binary opinions updating," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 52-76.
    11. Pavel KOVÁŘ & Martin PELIKÁN & Darina HEŘMANOVSKÁ & Ivan VRANA, 2014. "How to reach a compromise solution on technical and non-structural flood control measures," Soil and Water Research, Czech Academy of Agricultural Sciences, vol. 9(4), pages 143-152.
    12. Ulrich Faigle & Michel Grabisch, 2016. "Bases and linear transforms of TU-games and cooperation systems," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 875-892, November.
    13. Michel Grabisch & Agnieszka Rusinowska, 2016. "Determining models of influence," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 26(2), pages 69-85.
    14. Alexis Poindron, 2019. "A general model of synchronous updating with binary opinions," Post-Print halshs-02372486, HAL.
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    16. Alexis Poindron & Nizar Allouch, 2024. "A Model of Competing Gangs in Networks," Games, MDPI, vol. 15(2), pages 1-15, February.

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    More about this item

    Keywords

    influential coalition; social network; Influence; aggregation function; convergence; terminal class; réseau social; fonction d'agrégation;
    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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