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.
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Momo Kenfack, J.A., Tchantcho, B. & Tsague, B.P. On the ordinal equivalence of the Jonhston, Banzhaf and Shapley–Shubik power indices for voting games with abstention. Int J Game Theory 48, 647–671 (2019). https://doi.org/10.1007/s00182-018-0650-x
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DOI: https://doi.org/10.1007/s00182-018-0650-x