New algorithms compute power indices in weighted majority games, suggesting improved efficiency for calculations.
Power indices of weighted majority games are measures of the effects of parties on the voting in a council. Among the many kinds of power indices, Banzhaf index, Shapley-Shubik index and Deegan-Packel index have been studied well. For computing these power indices, dynamic programming algorithms had been proposed. The time complexities of these algorithms are O(n^2q), O(n^3q), and O(n^4q), respectively. We propose new algorithms for computing power indices, whose time complexities are O(nq), O(n^2q), and O(n^2q), respectively.
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Takeaki Uno (2003) studied this question.
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