We introduce a new axiom for power indices, which requires the total (additively aggregated) power of the voters to be nondecreasing in response to an expansion of the set of winning coalitions; the total power is thereby reflecting an increase in the collective power that such an expansion creates. It is shown that total-power monotonic indices that satisfy the standard semivalue axioms are probabilistic mixtures of generalized Coleman-Shapley indices, where the latter concept extends, and is inspired by, the notion introduced in Casajus and Huettner (Public choice, forthcoming, 2019 ). Generalized Coleman-Shapley indices are based on a version of the random-order pivotality that is behind the Shapley-Shubik index, combined with an assumption of random participation by players.

中文翻译：

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广义 Coleman-Shapley 指数和总功率单调性

我们为权力指数引入了一个新公理，它要求选民的总（加法聚合）权力不随着获胜联盟集的扩大而减少；因此，总权力反映了这种扩张所创造的集体权力的增加。结果表明，满足标准半值公理的总功率单调指数是广义 Coleman-Shapley 指数的概率混合，后者的概念扩展并受到 Casajus 和 Huettner 中引入的概念的启发（公共选择，即将出版，2019 ）。广义 Coleman-Shapley 指数基于 Shapley-Shubik 指数背后的随机顺序关键性版本，并结合玩家随机参与的假设。