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Solidarity Measures

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Transactions on Computational Collective Intelligence XXXVII

Part of the book series: Lecture Notes in Computer Science ((TCCI,volume 13750))

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Abstract

This paper regards some measures for sharing (public) goods or budgets among members with different participation quotas in a binary decision-making process. The main characteristic of such measures is that they should have elements of solidarity with those who have a weak quota of participation in the process. These measures seem appropriate for deals that require solidarity, which contrasts with the classical power indices such as the Shapley and Shubik index or the Banzhaf index. Moreover, we provide a new representation for two power indices—the Public Help Index ξ (proposed by Bertini and Stach in 2015) and the particularization of the solidarity value proposed by Nowak and Radzik in 1994—the ψ index—in a simple game using null player free winning coalitions. As it is known, a set of null player free winning coalitions unequivocally determines a simple game. Finally, we compare considered power indices considering some properties in simple games.

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Authors and Affiliations

  1. AGH University of Science and Technology, Al. Mickiewicza 30, 30-059, Krakow, Poland

    Izabella Stach

  2. Department of Economics, University of Bergamo, Via dei Caniana, 2, 24127, Bergamo, Italy

    Cesarino Bertini

Authors
  1. Izabella Stach
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  2. Cesarino Bertini
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Correspondence to Izabella Stach .

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Editors and Affiliations

  1. Institute of Informatics, Wroclaw University of Technology, Wroclaw, Poland

    Ngoc Thanh Nguyen

  2. Faculty of Information and Communication Technology, Swinburne University of Technology, Hawthorn, Victoria, VIC, Australia

    Ryszard Kowalczyk

  3. WSB University in Wroclaw, Wroclaw, Poland

    Jacek Mercik

  4. University of Lower Silesia, Wroclaw, Poland

    Anna Motylska-Kuźma

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Stach, I., Bertini, C. (2022). Solidarity Measures. In: Nguyen, N.T., Kowalczyk, R., Mercik, J., Motylska-Kuźma, A. (eds) Transactions on Computational Collective Intelligence XXXVII. Lecture Notes in Computer Science(), vol 13750. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-66597-8_5

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  • DOI: https://doi.org/10.1007/978-3-662-66597-8_5

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