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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, 2012. "On minimum sum representations for weighted voting games," Annals of Operations Research, Springer, vol. 196(1), pages 361-369, July.
    2. Martin, Mathieu & Nganmeni, Zephirin & Tchantcho, Bertrand, 2017. "The Owen and Shapley spatial power indices: A comparison and a generalization," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 10-19.
    3. De, Anindya & Diakonikolas, Ilias & Servedio, Rocco A., 2017. "The Inverse Shapley value problem," Games and Economic Behavior, Elsevier, vol. 105(C), pages 122-147.
    4. Felsenthal, Dan S & Machover, Moshe, 1996. "Alternative Forms of the Shapley Value and the Shapley-Shubik Index," Public Choice, Springer, vol. 87(3-4), pages 315-318, June.
    5. Kanazawa, Satoshi, 1998. "A brief note on a further refinement of the Condorcet Jury Theorem for heterogeneous groups," Mathematical Social Sciences, Elsevier, vol. 35(1), pages 69-73, January.
    6. Sascha Kurz & Nicola Maaser & Stefan Napel, 2017. "On the Democratic Weights of Nations," Journal of Political Economy, University of Chicago Press, vol. 125(5), pages 1599-1634.
    7. Pradeep Dubey & Lloyd S. Shapley, 1979. "Mathematical Properties of the Banzhaf Power Index," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 99-131, May.
    8. Ulrich Faigle & Michel Grabisch, 2016. "Bases and linear transforms of TU-games and cooperation systems," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 875-892, November.
    9. Xingwei Hu, 2006. "An Asymmetric Shapley–Shubik Power Index," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(2), pages 229-240, August.
    10. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    11. Delucchi, Mark A. & Jacobson, Mark Z., 2011. "Providing all global energy with wind, water, and solar power, Part II: Reliability, system and transmission costs, and policies," Energy Policy, Elsevier, vol. 39(3), pages 1170-1190, March.
    12. Rainer Hegselmann & Ulrich Krause, 2002. "Opinion Dynamics and Bounded Confidence Models, Analysis and Simulation," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 5(3), pages 1-2.
    13. Sascha Kurz, 2014. "Measuring Voting Power in Convex Policy Spaces," Economies, MDPI, vol. 2(1), pages 1-33, March.
    14. Robert T. Clemen & Robert L. Winkler, 1999. "Combining Probability Distributions From Experts in Risk Analysis," Risk Analysis, John Wiley & Sons, vol. 19(2), pages 187-203, April.
    15. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2009. "Aggregation functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445120, HAL.
    16. Nicola Maaser & Stefan Napel, 2007. "Equal representation in two-tier voting systems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(3), pages 401-420, April.
    17. Randall Holcombe, 1989. "The median voter model in public choice theory," Public Choice, Springer, vol. 61(2), pages 115-125, May.
    18. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
    19. Kay-Yut Chen & Leslie R. Fine & Bernardo A. Huberman, 2004. "Eliminating Public Knowledge Biases in Information-Aggregation Mechanisms," Management Science, INFORMS, vol. 50(7), pages 983-994, July.
    20. Joseph C. McMurray, 2013. "Aggregating Information by Voting: The Wisdom of the Experts versus the Wisdom of the Masses," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(1), pages 277-312.
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    Cited by:

    1. 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.
    2. 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.

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