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Measuring Power and Satisfaction in Societies with Opinion Leaders

Author

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  • René van den Brink

    (Department of Econometrics and Tinbergen 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

Opinion leaders are actors who have some power over their followers as they are able to influence their followers' choice of action in certain instances. In van den Brink et al. (2011) we proposed a two-action model for societies with opinion leaders. We introduced a power and a satisfaction score and studied some common properties. In this paper we strengthen two of these properties and present two further properties, which allows us to axiomatize both scores for the case that followers require unanimous action inclinations of their opinion leaders to follow them independently from their own action inclinations.

Suggested Citation

  • René van den Brink & Agnieszka Rusinowska & Frank Steffen, 2013. "Measuring Power and Satisfaction in Societies with Opinion Leaders," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00756720, HAL.
    • Handle: RePEc:hal:cesptp:hal-00756720
    DOI: 10.1007/s00355-012-0699-6
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    References listed on IDEAS

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    1. 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.
    2. René van den Brink & Agnieszka Rusinowska & Frank Steffen, 2013. "Measuring Power and Satisfaction in Societies with Opinion Leaders," Post-Print hal-00756720, HAL.
    3. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    4. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 89-99.
    5. Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(3), pages 261-281.
    6. René Brink & Frank Steffen, 2008. "Positional Power in Hierarchies," Springer Books, in: Matthew Braham & Frank Steffen (ed.), Power, Freedom, and Voting, chapter 4, pages 57-81, Springer.
    7. Matthew Braham, 2008. "Social Power and Social Causation: Towards a Formal Synthesis," Springer Books, in: Matthew Braham & Frank Steffen (ed.), Power, Freedom, and Voting, chapter 1, pages 1-21, Springer.
    8. Sitabhra Sinha & S. Raghavendra, 2006. "Emergence of two-phase behavior in markets through interaction and learning in agents with bounded rationality," Springer Books, in: Hideki Takayasu (ed.), Practical Fruits of Econophysics, pages 200-204, Springer.
    9. René Brink, 2010. "Axiomatizations of Banzhaf permission values for games with a permission structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(3), pages 445-466, July.
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    Cited by:

    1. René van den Brink & Agnieszka Rusinowska & Frank Steffen, 2013. "Measuring Power and Satisfaction in Societies with Opinion Leaders," PSE-Ecole d'économie de Paris (Postprint) hal-00756720, HAL.
    2. 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.
    3. Maurice Koster & Sascha Kurz & Ines Lindner & Stefan Napel, 2017. "The prediction value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 433-460, February.
    4. Sascha Kurz, 2014. "Measuring Voting Power in Convex Policy Spaces," Economies, MDPI, vol. 2(1), pages 1-33, March.
    5. Michel Grabisch & Agnieszka Rusinowska, 2010. "Different Approaches to Influence Based on Social Networks and Simple Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00514850, HAL.
    6. Encarnacion Algaba & René van den Brink & Chris Dietz, 2015. "Power Measures and Solutions for Games under Precedence Constraints," Tinbergen Institute Discussion Papers 15-007/II, Tinbergen Institute.
    7. 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.
    8. 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.
    9. René van den Brink & Frank Steffen, 2012. "On the Measurement of Success and Satisfaction," Tinbergen Institute Discussion Papers 12-030/1, Tinbergen Institute.
    10. Ibarzabal, Nora & Laruelle, Annick, 2018. "Ghost seats in parliaments," European Journal of Operational Research, Elsevier, vol. 264(1), pages 354-363.

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    Keywords

    power; satisfaction; axiomatization; Collective choice; follower; opinion leader;
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