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ACHIEVABLE HIERARCHIES IN VOTING GAMES

机译：投票游戏中可达到的等级

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摘要

Previous work by Diffo Lambo and Moulen [Theory and Decision 53, 313-325 (2002)] and Felsenthal and Machover [The Measurement of Voting Power, Edward Elgar Publishing Limited (1998)], shows that all swap preserving measures of voting power are ordinally equivalent on any swap robust simple voting game. Swap preserving measures include the Banzhaf, the Shapley-Shubik and other commonly used measures of a priori voting power. In this paper, we completely characterize the achievable hierarchies for any such measure on a swap robust simple voting game. Each possible hierarchy can be induced by a weighted voting game and we provide a constructive proof of this result. In particular, the strict hierarchy is always achievable as long as there are at least five players.
机译：Diffo Lambo和Moulen [理论和决策53，313-325（2002）]和Felsenthal和Machover [投票权的衡量，Edward Elgar Publishing Limited（1998）]的先前工作表明，所有保留投票权的掉期措施都是通常等效于任何可互换的简单投票游戏。交换保护措施包括Banzhaf，Shapley-Shubik和其他通常使用的先验投票权措施。在本文中，我们完全刻画了掉期稳健的简单投票博弈中任何此类度量的可实现层次结构。加权投票博弈可以诱发每个可能的层次结构，我们提供了有关此结果的建设性证明。特别是，只要至少有五个参与者，就始终可以实现严格的等级制度。

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