Competition between a complex system's constituents and a correspondingreward mechanism based on it have profound influence on the functioning,stability, and evolution of the system. But determining the dominance hierarchyor ranking among the constituent parts from the strongest to the weakest --essential in determining reward or penalty -- is almost always an ambiguoustask due to the incomplete nature of competition networks. Here we introduce``Natural Ranking," a desirably unambiguous ranking method applicable to acomplete (full) competition network, and formulate an analytical model based onthe Bayesian formula inferring the expected mean and error of the naturalranking of nodes from an incomplete network. We investigate its potential anduses in solving issues in ranking by applying to a real-world competitionnetwork of economic and social importance.
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