Weighted voting games model decision-making\u00a0bodies where decisions are made by a majority\u00a0vote. In such games, each agent has a weight, and\u00a0a coalition of agents wins the game if the sum of\u00a0the weights of its members exceeds a certain quota.\u00a0The Shapley value is used as an index for the true\u00a0power held by the agents in such games.\u00a0Earlier work has studied the implications of setting\u00a0the value of the quota on the agents\u2019 power under\u00a0the assumption that the game is given with a fixed\u00a0set of agent weights. We focus on a model where\u00a0the agent weights originate from a stochastic process,\u00a0resulting in weight uncertainty. We analyze\u00a0the expected effect of the quota on voting power
\ngiven the weight generating process. We examine\u00a0two extreme cases of the balls and bins model: uniform\u00a0and exponentially decaying probabilities. We\u00a0show that the choice of a quota may have a large\u00a0influence on the power disparity of the agents, even\u00a0when the governing distribution is likely to result in\u00a0highly similar weights for the agents. We characterize\u00a0various interesting repetitive fluctuation patterns\u00a0in agents\u2019 power as a function of the quota.<\/p>\n","protected":false},"excerpt":{"rendered":"
Weighted voting games model decision-making\u00a0bodies where decisions are made by a majority\u00a0vote. In such games, each agent has a weight, and\u00a0a coalition of agents wins the game if the sum of\u00a0the weights of its members exceeds a certain quota.\u00a0The Shapley value is used as an index for the true\u00a0power held by the agents in such […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"IJCAI","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"IJCAI 2016","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"IJCAI 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