  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 the 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.
