What question did this study set out to answer?

The aim is to improve the computational efficiency of power indices in weighted majority games.

April 1, 2026Open Access

NII Technical Report (NII-2003-006E)：Efficient Computation of Power Indices for Weighted Majority Games

Key Points

The aim is to improve the computational efficiency of power indices in weighted majority games.
Develop new algorithms for computing power indices.
Analyze time complexities of proposed algorithms compared to existing ones.
Focus on Banzhaf index, Shapley-Shubik index, and Deegan-Packel index.
Introduced algorithms with time complexities of O(nq), O(n^2q), and O(n^2q).
Demonstrated improvement over existing algorithms with higher time complexities.

Abstract

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 (n²q), O (n³q), and O (n⁴q), respectively. We propose new algorithms for computing power indices, whose time complexities are O (nq), O (n²q), and O (n²q), respectively.

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Cite This Study

Takeaki Uno (Fri,) studied this question.

synapsesocial.com/papers/69cd7a4e5652765b073a7524 https://doi.org/https://doi.org/10.20736/0000000387

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