Simple Majority Achievable Hierarchies

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We completely characterize the simple majority weighted voting game achievable hierarchies, and, in doing so, show that a problem about representative government, noted by J. Banzhaf [Rutgers Law Review58, 317–343 (1965)] cannot be resolved using the simple majority quota. We also demonstrate that all hierarchies achievable by any quota can be achieved if the simple majority quota is simply incremented by one.

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