NP-completeness of some problems concerning voting games
International Journal of Game Theory
On the complexity of cooperative solution concepts
Mathematics of Operations Research
NP-completeness for calculating power indices of weighted majority games
Theoretical Computer Science
A linear approximation method for the Shapley value
Artificial Intelligence
Note: The complexity of power-index comparison
Theoretical Computer Science
Manipulating the quota in weighted voting games
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Approximating power indices: theoretical and empirical analysis
Autonomous Agents and Multi-Agent Systems
False-name manipulations in weighted voting games
Journal of Artificial Intelligence Research
Manipulating the quota in weighted voting games
Artificial Intelligence
On random quotas and proportional representation in weighted voting games
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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In weighted voting games, each agent has a weight, and a coalition of players is deemed to be winning if its weight meets or exceeds the given quota. An agent's power in such games is usually measured by her Shapley value, which depends both on the agent's weight and the quota. [Zuckerman et al., 2008] show that one can alter a player's power significantly by modifying the quota, and investigate some of the related algorithmic issues. In this paper, we answer a number of questions that were left open by [Zuckerman et al., 2008]: we show that, even though deciding whether a quota maximizes or minimizes an agent's Shapley value is coNP-hard, finding a Shapley value-maximizing quota is easy. Minimizing a player's power appears to be more difficult. However, we propose and evaluate a heuristic for this problem, which takes into account the voter's rank and the overall weight distribution. We also explore a number of other algorithmic issues related to quota manipulation.