We study the Shapley value in weighted voting games. The Shapley value has been used as an index for measuring the power of individual agents in decision-making bodies and political organizations, where decisions are made by a majority vote process. We characterize the impact of changing the quota (i.e., the minimum number of seats in the parliament that are required to form a coalition) on the Shapley values of the agents. Contrary to previous studies, which assumed that the agent weights (corresponding to the size of a caucus or a political party) are fixed, we analyze new domains in which the weights are stochastically generated, modelling, for example, elections processes.
We examine a natural weight generation process: the Balls and Bins model, with uniform as well as exponentially decaying probabilities. We also analyze weights that admit a super-increasing sequence, answering several open questions pertaining to the Shapley values in such games.
Beyond Lower Quota: Avoiding Overrepresentation in Multi-Winner Voting
University of Warwick（华威大学）；University of Applied Sciences St. Pölten（圣珀尔滕应用科技大学）；WU Vienna University of Economics and Business（维也纳经济与商业大学）；TU Wien（维也纳工业大学）；Shanghai University of Finance and Economics（上海财经大学）
加权投票博弈（WVG）是一种联盟博弈，其中代理人对联盟的贡献由他的权重给出，如果联盟的总权重达到或超过给定的配额，则联盟获胜。这些游戏模型的决策，在政治机构以及合作和盈余分割多智能体域。近年来，加权投票博弈的各种解概念的计算复杂性受到了广泛的关注。特别是，Elkind et al.（2007）研究了WVG中与稳定性相关的解决方案概念的复杂性，即核心，最小核心和核仁。虽然他们已经完全描述了核心和最小核心的算法复杂性，但对于核仁，他们只提供了NP-硬度结果。在本文中，我们解决了Elkind等人提出的一个公开问题。通过证明WVG的核仁，以及更一般地，具有固定k的k-向量加权投票游戏，可以在伪多项式时间内计算，即，存在一种算法，其正确地计算核仁并且在玩家数量和最大权重的时间多项式中运行。在这样做的时候，我们提出了一个计算核仁，这可能是适用于更广泛的一类游戏的一般框架。
Voting power in the Council of the European Union: A comprehensive sensitivity analysis
Central Bank of Hungary（匈牙利国家银行）；Budapest Metropolitan University, MNB Institute（布达佩斯都会大学，MNB研究所）；Institute for Computer Science and Control (SZTAKI), Hungarian Research Network (HUN-REN)（计算机科学与控制研究所（SZTAKI），匈牙利研究网络（HUN-REN））；Laboratory on Engineering and Management Intelligence, Research Group of Operations Research and Decision Systems（工程与管理智能实验室，运筹学与决策系统研究组）；Corvinus University of Budapest (BCE), Institute of Operations and Decision Sciences, Department of Operations Research and Actuarial Sciences（布达佩斯考文纽斯大学（BCE），运营与决策科学研究所，运筹学与精算科学系）
