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All Power Structures are Achievable in Basic Weighted Games

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Advances in Collective Decision Making

Part of the book series: Studies in Choice and Welfare ((WELFARE))

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Abstract

A major problem in decision-making is designing voting systems that are as simple as possible and able to reflect a given hierarchy of power of its members. It is known that in the class of weighted games, all hierarchies are achievable except two of them. However, many weighted games are either improper or do not admit a minimum representation in integers or do not assign a minimum weight of 1 to the weakest non-null players. These factors prevent obtaining a good representation. The purpose of the paper is to prove that for each achievable hierarchy for weighted games, there is a handy weighted game fulfilling these three desirable properties. A representation of this type is ideal for the design of a weighted game with a given hierarchy. Moreover, the subclass of weighted games with these properties is considerably smaller than the class of weighted games.

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Acknowledgements

This publication is part of the I+D+i project / PID2019-104987GB-I00, financed by MCIN/ AEI/10.13039/501100011033/

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Authors and Affiliations

  1. Departament de Matemàtiques i Escola Politècnica Superior d’Enginyeria de Manresa, Universitat Politècnica de Catalunya, Manresa, Spain

    Josep Freixas & Montserrat Pons

Authors
  1. Josep Freixas
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  2. Montserrat Pons
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Correspondence to Josep Freixas .

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Editors and Affiliations

  1. Institute of Mathematics, University of Bayreuth, Bayreuth, Germany

    Sascha Kurz

  2. Department of Economics and Business Economics, Aarhus University, Aarhus, Denmark

    Nicola Maaser

  3. Department of Economics, University of Bayreuth, Bayreuth, Germany

    Alexander Mayer

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Freixas, J., Pons, M. (2023). All Power Structures are Achievable in Basic Weighted Games. In: Kurz, S., Maaser, N., Mayer, A. (eds) Advances in Collective Decision Making. Studies in Choice and Welfare. Springer, Cham. https://doi.org/10.1007/978-3-031-21696-1_9

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