Given a system where the real-valued states of the agents are aggregated by a function to a real-valued state of the entire system, we are interested in the influence or importance of different agents for that function. This generalizes the notion of power indices for binary voting systems to decisions over interval policy spaces and has applications in economics, engineering, security analysis, and other disciplines. Here, we study the question of importance in systems with interval decisions. Based on the classical Shapley–Shubik and Penrose–Banzhaf index, from binary voting, we motivate and analyze two importance measures. Additionally, we present some results for parametric classes of aggregation functions.

中文翻译：

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间隔决策系统的重要性

给定一个系统，其中代理的实值状态由一个函数聚合为整个系统的实值状态，我们感兴趣的是不同代理对该函数的影响或重要性。这将二元投票系统的权力指数概念推广到区间策略空间的决策，并在经济学、工程、安全分析和其他学科中有应用。在这里，我们研究了具有区间决策的系统中的重要性问题。基于经典的 Shapley-Shubik 和 Penrose-Banzhaf 指数，从二元投票中，我们激发和分析了两个重要性度量。此外，我们提供了一些聚合函数参数类的结果。