Characterization of the Shapley-Shubik Power Index Without the Efficiency Axiom
We show that the Shapley-Shubik power index on the domain of simple (voting) games can be uniquely characterized without the e¢ ciency axiom. In our axiomatization, the efficiency is replaced by the following weaker require- ment that we term the gain-loss axiom: any gain in power by a player implies a loss for someone else (the axiom does not specify the extent of the loss). The rest of our axioms are standard: transfer (which is the version of additivity adapted for simple games), symmetry or equal treatment, and dummy
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- Dubey, Pradeep & Einy, Ezra & Haimanko, Ori, 2005. "Compound voting and the Banzhaf index," Games and Economic Behavior, Elsevier, vol. 51(1), pages 20-30, April.
- Blair, Douglas H. & McLean, Richard P., 1990. "Subjective evaluations of n-person games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 346-361, April.
- Roth, Alvin E., 1977. "Utility functions for simple games," Journal of Economic Theory, Elsevier, vol. 16(2), pages 481-489, December.
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