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Research Report CS-RR-437

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Haris Aziz and Mike Paterson, Variation in Weighted Voting Games

Weighted voting games are ubiquitous mathematical models which are used in economics, political science, neuroscience, threshold logic, reliability theory and distributed systems. They model situations where agents with variable voting weight vote in favour of or against a decision. A coalition of agents is winning if and only if the sum of weights of the coalition exceeds or equals a specified quota. Tolerance and amplitude of a weighted voting game signify the possible variations in a weighted voting game which still keep the game unchanged. We characterize the complexity of computing the tolerance and amplitude of weighted voting games. We give tighter bounds and results for the tolerance and amplitude of key weighted voting games. We then provide limits to how much the Banzhaf index of a player increases or decreases if it splits up into sub-players.

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