The polynomial-time hierarchy and sparse oracles
Journal of the ACM (JACM)
The complexity of optimization problems
Journal of Computer and System Sciences - Structure in Complexity Theory Conference, June 2-5, 1986
NP-completeness of some problems concerning voting games
International Journal of Game Theory
PP is as hard as the polynomial-time hierarchy
SIAM Journal on Computing
On the complexity of cooperative solution concepts
Mathematics of Operations Research
The Complexity of Planar Counting Problems
SIAM Journal on Computing
Power balance and apportionment algorithms for the United States Congress
Journal of Experimental Algorithmics (JEA)
Rank aggregation methods for the Web
Proceedings of the 10th international conference on World Wide Web
NP-completeness for calculating power indices of weighted majority games
Theoretical Computer Science
On Different Reducibility Notions for Function Classes
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
On Some Central Problems in Computational Complexity
On Some Central Problems in Computational Complexity
Divide and conquer: false-name manipulations in weighted voting games
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Proceedings of the 2010 conference on STAIRS 2010: Proceedings of the Fifth Starting AI Researchers' Symposium
False-name manipulations in weighted voting games
Journal of Artificial Intelligence Research
Manipulating the quota in weighted voting games
Artificial Intelligence
The Shapley value as a function of the quota in weighted voting games
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
On random quotas and proportional representation in weighted voting games
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Sharing rewards in cooperative connectivity games
Journal of Artificial Intelligence Research
| Hi-index | 5.23 |
We study the complexity of the following problem: Given two weighted voting games G^' and G^'' that each contain a player p, in which of these games is p's power index value higher? We study this problem with respect to both the Shapley-Shubik power index and the Banzhaf power index. Our main result is that for both of these power indices the problem is complete for probabilistic polynomial time (i.e., is PP-complete). We apply our results to partially resolve some recently proposed problems regarding the complexity of weighted voting games. We also study the complexity of the raw Shapley-Shubik power index. Deng and Papadimitriou showed that the raw Shapley-Shubik power index is #P-metric-complete. We strengthen this by showing that the raw Shapley-Shubik power index is many-one complete for #P. And our strengthening cannot possibly be further improved to parsimonious completeness, since we observe that, in contrast with the raw Banzhaf power index, the raw Shapley-Shubik power index is not #P-parsimonious-complete.