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Lattices in social networks with influence

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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

We present an application of lattice theory to the framework of influence in social networks. The contribution of the paper is not to derive new results, but to synthesize our existing results on lattices and influence. We consider a two-action model of influence in a social network in which agents have to make their yes-no decision on a certain issue. Every agent is preliminarily inclined to say either 'yes' or 'no', but due to influence by others, the agent's decision may be different from his original inclination. We discuss the relation between two central concepts of this model: influence function and follower function. The structure of the set of all influence functions that lead to a given follower function appears to be a distributive lattice. We also consider a dynamic model of influence based on aggregation functions and present a general analysis of convergence in the model. Possible terminal classes to which the process of influence may converge are terminal states (the consensus states and non trivial states), cyclic terminal classes and unions of Boolean lattices.

Suggested Citation

  • Michel Grabisch & Agnieszka Rusinowska, 2015. "Lattices in social networks with influence," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00977005, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00977005
    DOI: 10.1142/S0219198915400046
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00977005
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    References listed on IDEAS

    as
    1. Monjardet, Bernard, 2003. "The presence of lattice theory in discrete problems of mathematical social sciences. Why," Mathematical Social Sciences, Elsevier, vol. 46(2), pages 103-144, October.
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    8. Michel Grabisch & Agnieszka Rusinowska, 2009. "Influence in social networks," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00496556, HAL.
    9. Adrian van Deemen & Agnieszka Rusinowska, 2010. "Collective Decision Making: Views from Social Choice and Game Theory," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00514840, HAL.
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    More about this item

    Keywords

    convergence; terminal class; aggregation function; Influence function; follower function; distributive lattice;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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