Urnings: A New Method for Tracking Dynamically Changing Parameters in Paired Comparison Systems

Abstract We introduce a new rating system for tracking the development of parameters based on stream observations that can be viewed as paired comparisons. Rating systems are applied in competitive games, adaptive learning and platforms product service reviews. model each observation an outcome game chance depends interest (e.g. chess abilities two players). Determining probabilities different outcomes is conceptualized urn problem, where represented by probability (i.e. proportion balls urn). This setup allows evaluating standard errors ratings performing statistical inferences about of, relations between, parameters. Theoretical properties terms invariant distributions their convergence derived. The illustrated with simulated examples its potential answering research questions using data from chess, movie review system, math.