On the ordinal equivalence of the Jonhston, Banzhaf and Shapley–Shubik power indices for voting games with abstention

Joseph Armel Momo Kenfack (), Bertrand Tchantcho () and Bill Proces Tsague ()
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Joseph Armel Momo Kenfack: The University of Yaoundé I (MASS)
Bertrand Tchantcho: The University of Yaoundé I (MASS)
Bill Proces Tsague: The University of Yaoundé I (MASS)

International Journal of Game Theory, 2019, vol. 48, issue 2, No 13, 647-671

Abstract: Abstract The aim of this paper is twofold. We extend the well known Johnston power index usually defined for simple voting games, to voting games with abstention and we provide a full characterization of this extension. On the other hand, we conduct an ordinal comparison of three power indices: the Shapley–Shubik, Banzhaf and newly defined Johnston power indices. We provide a huge class of voting games with abstention in which these three power indices are ordinally equivalent. This is clearly a generalization of the work by Freixas et al. (Eur J Oper Res 216:367–375, 2012) and a twofold extension of Parker (Games Econ Behav 75:867–881, 2012) in the sense that, the ordinal equivalence emerges for three power indices (not just for the Shapley–Shubik and the Banzhaf indices), and it holds for a class of games strictly larger than the class of I-complete (3,2) games namely semi I-complete (3,2) games.

Keywords: Power indices; Ordinal equivalence; Abstention; (3; 2) voting games; Axiomatic characterization; 91A12; 05C65; 94C10 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00182-018-0650-x

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