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Axiomatizations for the Shapley-Shubik power index for games with several levels of approval in the input and output

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arxiv 2001.10197 v1 pith:3SCDE3XH submitted 2020-01-28 cs.GT

Sascha Kurz , Issofa Moyouwou , Hilaire Touyem This is my paper · ORCID
classification cs.GT
keywords gamesindexshapley-shubikapprovaldecisionsinputlevelsoutput
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abstract

The Shapley-Shubik index is a specialization of the Shapley value and is widely applied to evaluate the power distribution in committees drawing binary decisions. It was generalized to decisions with more than two levels of approval both in the input and the output. The corresponding games are called $(j,k)$ simple games. Here we present a new axiomatization for the Shapley-Shubik index for $(j,k)$ simple games as well as for a continuous variant, which may be considered as the limit case.

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