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Importance In Systems With Interval Decisions

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  • SASCHA KURZ

    (Department of Mathematics, University of Bayreuth, Universitätsstr. 30, 95440 Bayreuth, Germany)

Abstract

Given a system where the real-valued states of the agents are aggregated by a function to a real-valued state of the entire system, we are interested in the influence or importance of different agents for that function. This generalizes the notion of power indices for binary voting systems to decisions over interval policy spaces and has applications in economics, engineering, security analysis, and other disciplines. Here, we study the question of importance in systems with interval decisions. Based on the classical Shapley–Shubik and Penrose–Banzhaf index, from binary voting, we motivate and analyze two importance measures. Additionally, we present some results for parametric classes of aggregation functions.

Suggested Citation

  • Sascha Kurz, 2018. "Importance In Systems With Interval Decisions," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 21(06n07), pages 1-23, September.
    • Handle: RePEc:wsi:acsxxx:v:21:y:2018:i:06n07:n:s0219525918500248
    DOI: 10.1142/S0219525918500248
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    References listed on IDEAS

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    1. Sascha Kurz & Issofa Moyouwou & Hilaire Touyem, 2021. "Axiomatizations for the Shapley–Shubik power index for games with several levels of approval in the input and output," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(3), pages 569-594, April.
    2. Jan Lorenz & Martin Neumann, 2018. "Opinion Dynamics And Collective Decisions," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 21(06n07), pages 1-9, September.

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