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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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  • 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.
    • Handle: RePEc:kap:theord:v:69:y:2010:i:4:p:635-656
    DOI: 10.1007/s11238-009-9150-6
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    Citations

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    Cited by:

    1. Grabisch, Michel & Rusinowska, Agnieszka, 2013. "A model of influence based on aggregation functions," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 316-330.
    2. 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.
    3. 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).
    4. Pongou, Roland & Tchantcho, Bertrand & Tedjeugang, Narcisse, 2014. "Power theories for multi-choice organizations and political rules: Rank-order equivalence," Operations Research Perspectives, Elsevier, vol. 1(1), pages 42-49.
    5. 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.
    6. Ushchev, Philip & Zenou, Yves, 2020. "Social norms in networks," Journal of Economic Theory, Elsevier, vol. 185(C).
    7. 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.
    8. Sascha Kurz, 2014. "Measuring Voting Power in Convex Policy Spaces," Economies, MDPI, vol. 2(1), pages 1-33, March.
    9. David Lowing & Kevin Techer, 2022. "Marginalism, egalitarianism and efficiency in multi-choice games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(4), pages 815-861, November.
    10. René 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.
    11. 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.
    12. David Lowing & Kevin Techer, 2021. "Marginalism, Egalitarianism and E ciency in Multi-Choice Games," Working Papers halshs-03334056, HAL.
    13. Michel Grabisch & Agnieszka Rusinowska, 2009. "A model of influence with a continuum of actions," Post-Print halshs-00464460, HAL.

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