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