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Generalizing and Modifying the Hoede-Bakker Index

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Theory and Applications of Relational Structures as Knowledge Instruments II

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4342))

Abstract

In this paper, we generalize the Hoede-Bakker index, which is a measure for the power of agents in a network, taking into account the mutual influences of the agents. We adopt sets of axioms different from the one adopted in the original definition. In particular, we remove an original assumption according to which changing all inclinations of the players leads to the opposite group decision. Several examples showing the usefulness of this generalization are constructed. In particular, we may apply the generalized Hoede-Bakker index to a game with a vetoer. Next, the relation between the generalized Hoede-Bakker index and the Penrose measure is analysed. Moreover, we introduce several modifications of the Hoede-Bakker index which lead to the Coleman indices, the Rae index, and the König-Bräuninger index. In order to show the relation between the generalized or the modified Hoede-Bakker index and the other power indices, we use the probabilistic approach.

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Author information

Authors and Affiliations

  1. Nijmegen School of Management, Radboud University Nijmegen, P.O. Box 9108, 6500, HK, Nijmegen, The Netherlands

    Agnieszka Rusinowska

  2. Department of Mathematical Economics, Warsaw School of Economics, Al. Niepodleglosci 162, 02-554, Warsaw, Poland

    Agnieszka Rusinowska

  3. Faculty of Philosophy, Tilburg University, P.O. Box 90153, 5000, LE Tilburg, The Netherlands

    Harrie de Swart

Authors
  1. Agnieszka Rusinowska
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  2. Harrie de Swart
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Editors and Affiliations

  1. Faculty of Philosophy, Tilburg University, P.O. Box 90153, 5000, Tilburg, LE, The Netherlands

    Harrie de Swart

  2. National Institute of Telecommunications, Warsaw,  

    Ewa Orłowska

  3. Institute for Software Technology, Department of Computing Science, Universität der Bundeswehr München, 85577, Neubiberg, Germany

    Gunther Schmidt

  4. Faculté Polytechnique de Mons, Rue de Houdain 9, B-7000, Mons, Belgium

    Marc Roubens

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Rusinowska, A., de Swart, H. (2006). Generalizing and Modifying the Hoede-Bakker Index. In: de Swart, H., Orłowska, E., Schmidt, G., Roubens, M. (eds) Theory and Applications of Relational Structures as Knowledge Instruments II. Lecture Notes in Computer Science(), vol 4342. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11964810_4

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  • DOI: https://doi.org/10.1007/11964810_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69223-2

  • Online ISBN: 978-3-540-69224-9

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