Abstract
When analyzing mathematically decision mechanisms ruled by voting it is sometimes convenient to include abstention as a possible alternative for the voters. In classical simple games, abstention, if considered, is formally equivalent to voting against the proposal. Simple games with alternatives are useful to study voting systems where abstention does not favour any of the options. In this work, we axiomatically characterize the Shapley–Shubik index for simple games with alternatives and apply it to an example taken from real life.
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This work has been partially supported by Grant MTM 2006–06064 of the Education and Science Spanish Ministry and the European Regional Development Fund, and Grant SGR 2005–00651 of the Catalonia Government.
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Carreras, F., Magaña, A. The Shapley–Shubik index for simple games with multiple alternatives. Ann Oper Res 158, 81–97 (2008). https://doi.org/10.1007/s10479-007-0246-5
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DOI: https://doi.org/10.1007/s10479-007-0246-5