Generalized Coleman-Shapley indices and total-power monotonicity

We introduce a new axiom for power indices, which requires the total (additively aggregated) power of the voters to be nondecreasing in response to an expansion of the set of winning coalitions; the total power is thereby reflecting an increase in the collective power that such an expansion creates....

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Bibliographic Details
Published in:International journal of game theory 2020-03, Vol.49 (1), p.299-320
Main Author: Haimanko, Ori
Format: Article
Language:English
Subjects:
Axioms
Behavioral/Experimental Economics
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Game Theory
Mixtures
Operations Research/Decision Theory
Original Paper
Power
Public choice
Social and Behav. Sciences
Voters
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Summary:We introduce a new axiom for power indices, which requires the total (additively aggregated) power of the voters to be nondecreasing in response to an expansion of the set of winning coalitions; the total power is thereby reflecting an increase in the collective power that such an expansion creates. It is shown that total-power monotonic indices that satisfy the standard semivalue axioms are probabilistic mixtures of generalized Coleman-Shapley indices, where the latter concept extends, and is inspired by, the notion introduced in Casajus and Huettner (Public choice, forthcoming, 2019 ). Generalized Coleman-Shapley indices are based on a version of the random-order pivotality that is behind the Shapley-Shubik index, combined with an assumption of random participation by players.
ISSN:0020-7276
1432-1270
DOI:10.1007/s00182-019-00692-2