Abstract
One assumption in the Shapley–Shubik power index is that there is no interaction nor influence among the voting members. This paper will apply the command structure of Shapley (1994) to model members' interaction relations by simple games. An equilibrium authority distribution is then formulated by the power-in/power-out mechanism. It turns out to have much similarity to the invariant measure of a Markov chain and therefore some similar interpretations are followed for the new setting. In some sense, one's authority distribution quantifies his general administrative power in the organization and his long-run influence on all members. We provide a few applications in conflict resolution, college and journal ranking, and organizational choice.
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