Abstract
(1978) proposed a number valued index that measures the power that individual voters have in a simple voting game. In this paper we show that the influence (or desirability) relation introduced by Isbell (1958) is a sub-preordering of the Johnston index for every simple voting game. Furthermore, the preorderings induced by the Johnston, Shapley-Shubik and Banzhaf-Coleman indices coincide if and only if the simple voting game is swap robust.
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Roy, S. (2010). The Ordinal Equivalence of the Johnston Index and the Established Notions of Power. In: Basu, B., Chakravarty, S.R., Chakrabarti, B.K., Gangopadhyay, K. (eds) Econophysics and Economics of Games, Social Choices and Quantitative Techniques. New Economic Windows. Springer, Milano. https://doi.org/10.1007/978-88-470-1501-2_35
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DOI: https://doi.org/10.1007/978-88-470-1501-2_35
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-1500-5
Online ISBN: 978-88-470-1501-2
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