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The cost of principles

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We consider a variant of weighted voting games (WVGs) in which not all agents are willing to co-operate with each other. In a WVG each agent has a weight, and a set of agents can form a winning coalition if the sum of their weights exceeds a given quota (for example the formation of a coalition government from political parties who each have a number parliamentary seats is a WVG ). The original WVG model assumes that all coalitions are possible, i.e. all agents are compatible. In contrast, we consider a model in which the agents’ compatibility is described by a “compatibility graph”. We generalise the Shapley-Shubik and Banzhaf power indices in order to measure power in this new setting. We consider the computational aspects of calculating the power indices, and show that this is tractable when the agents’ compatibilities are defined by “single peaked preference”. Through simulations we investigate the effect an agent’s compatibility restrictions has on its power.

This talk is part of the Microsoft Research Machine Learning and Perception Seminars series.

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