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A generalization of the coherent-noise models [M. E. J. Newman and K.Sneppen, Phys. Rev. E{\bf54}, 6226 (1996)] is presented where the agents in themodel are subjected to a multitude of stresses, generated in a hierarchy ofdifferent contexts. The hierarchy is realized as a Cayley-tree. Two differentways of stress propagation in the tree are considered. In both cases, coherencearises in large subsystems of the tree. Clear similarities between the behaviorof the tree model and of the coherent-noise model can be observed. For one ofthe two methods of stress propagation, the behavior of the tree model can beapproximated very well by an ensemble of coherent-noise models, where the sizes$k$ of the systems in the ensemble scale as $k^{-2}$. The results are found tobe independent of the tree's structure for a large class of reasonable choices.Additionally, it is found that power-law distributed lifetimes of agents ariseeven under the complete absence of correlations between the stresses the agentsfeel.Comment: 10 pages RevTeX, including 11 figures, to appear in Phys. Rev. E  (scheduled for December 1998). Calculations are more compact (for more  detailed calculations, see v1). Some more numerical data has been adde

Hierarchical noise in large systems of independent agents