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Measuring Power and Satisfaction in Societies with Opinion Leaders: Dictator and Opinion Leader Properties

Author

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  • René van den Brink

    (Department of Econometrics - Timbergen Institute - VU - Vrije Universiteit Amsterdam [Amsterdam])

  • Agnieszka Rusinowska

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

  • Frank Steffen

    (University of Liverpool)

Abstract

A well known and established model in communication policy in sociology and marketing is that of opinion leadership. Opinion leaders are actors in a society who are able to affect the behavior of other members of the society called followers. Hence, opinion leaders might have a considerable impact on the behavior of markets and other social agglomerations being made up of individual actors choosing among a number of alternatives. For marketing or policy purposes it appears to be interesting to investigate the effect of different opinion leader-follower structures in markets or any other collective decision-making situations in a society. We study a two-action model in which the members of a society are to choose one action, for instance, to buy or not to buy a certain joint product, or to vote yes or no on a specific proposal. Each of the actors has an inclination to choose one of the actions. By definition opinion leaders have some power over their followers, and they exercise this power by influencing the behavior of their followers, i.e. their choice of action. After all actors have chosen their actions, a decision-making mechanism determines the collective choice resulting out of the individual choices. Making use of bipartite digraphs we introduce novel satisfaction and power scores which allow us to analyze the actors' satisfaction and power with respect to the collective choice for societies with different opinion leader-follower structures. Moreover, we study common dictator and opinion leader properties of the above scores and illustrate our findings for a society with five members.

Suggested Citation

  • René van den Brink & Agnieszka Rusinowska & Frank Steffen, 2011. "Measuring Power and Satisfaction in Societies with Opinion Leaders: Dictator and Opinion Leader Properties," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00633881, HAL.
  • Handle: RePEc:hal:cesptp:hal-00633881
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    References listed on IDEAS

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    1. 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.
    2. Francis Aniefiok Bassey & John Nsikan Efiok & Okon & Saviour Sylvester & Inegbedion Daniel Osemudiamen, 2015. "Opinion Leadership and Marketing of Life Assurance in Selected Insurance Firms in Nigeria," International Journal of Empirical Finance, Research Academy of Social Sciences, vol. 4(3), pages 131-141.
    3. René Brink & Agnieszka Rusinowska & Frank Steffen, 2013. "Measuring power and satisfaction in societies with opinion leaders: an axiomatization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 671-683, September.
    4. René van den Brink, 2009. "Comparable Axiomatizations of the Myerson Value, the Restricted Banzhaf Value, Hierarchical Outcomes and the Average Tree Solution for Cycle-Free Graph Restricted Games," Tinbergen Institute Discussion Papers 09-108/1, Tinbergen Institute.
    5. Michel Grabisch & Agnieszka Rusinowska, 2010. "Different Approaches to Influence Based on Social Networks and Simple Games," Post-Print hal-00514850, HAL.
    6. Gusev, Vasily V., 2020. "The vertex cover game: Application to transport networks," Omega, Elsevier, vol. 97(C).
    7. René van den Brink & Frank Steffen, 2012. "On the Measurement of Success and Satisfaction," Tinbergen Institute Discussion Papers 12-030/1, Tinbergen Institute.

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    More about this item

    Keywords

    Bipartite digraph; influence; inclination; collective choice; opinion leader; follower; satisfaction; power; dictator properties; opinion leader properties;
    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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