Representation-Compatible Power Indices
28 Pages Posted: 20 Jun 2015
Date Written: June 19, 2015
This paper studies power indices based on average representations of a weighted game. If restricted to account for the lack of power of dummy voters, average representations become coherent measures of voting power, with power distributions being proportional to the distribution of weights in the average representation. This makes these indices representation-compatible, a property not fulfilled by classical power indices. Average representations can be tailored to reveal the equivalence classes of voters defined by the Isbell desirability relation, which leads to a pair of new power indices that ascribes equal power to all members of an equivalence class.
Keywords: average representation, power index, proportionality between weights and power
JEL Classification: D72
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