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

Importance in systems with interval decisions