Order transmission efficiency in large hierarchical organizations

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Abstract
We consider the elements in a, hierarchical organization (i.e. the decision-maker, the order transmitters and the executors) and their interdependence as described by a set of dependent random variables. An order corresponds to a specific value of the top random variable. Using the notions of conditional expectation and mutual information in a transmission channel, we introduce definitions for the operating cost and for the order transmission efficiency of the organization. We study how this efficiency is influenced by the number of hierarchical levels, by the number of degrees of freedom of the executors and by the existence of subformal communication (as opposed to official). The main conclusions are: (1) to improve efficiency, the hierarchy should be made as flat as possible ; (2) total control is almost always much too expensive ; and (3) subformal communication can either enhance or degrade efficiency ; examples of each kind are provided.

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