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Axiomatization of some power indices in voting games with abstention

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  • Joseph Siani

    (IESEG School of Management, UMR 9221-LEM-Lille Economie Management
    Univ. Lille, UMR 9221-LEM-Lille Economie Management
    CNRS, UMR 9221-LEM-Lille Economie Management)

  • Bertrand Tchantcho

    (University of Yaounde I
    Univ. Cergy-Pontoise, CNRS, UMR 8184-THEMA)

  • Bill Proces Tsague

    (University of Yaounde I)

Abstract

Power measures are used to quantify the influence of members of a democratic institution. We consider voting games with abstention or (3,2) games, which are decision-making processes in which voting options include yes, no and abstention. The power indices that we study are based on the notions of minimal and shift minimal winning tripartitions. We define and characterize the Deegan–Packel and shift Deegan–Packel power indices in the class of (3,2) games. Furthermore, owing to the parameterization result obtained by Freixas et al. (Discret Appl Math 255:21–39, 2019), we provide computational formulae of these indices in the class of I-complete (3,2) games. These formulae allow us to determine the power of each player in a game, regardless of the number of minimal and/or shift minimal winning tripartitions of the game.

Suggested Citation

  • Joseph Siani & Bertrand Tchantcho & Bill Proces Tsague, 2024. "Axiomatization of some power indices in voting games with abstention," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 62(4), pages 761-783, June.
    • Handle: RePEc:spr:sochwe:v:62:y:2024:i:4:d:10.1007_s00355-024-01517-2
    DOI: 10.1007/s00355-024-01517-2
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