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Urnings: A new method for tracking dynamically changing parameters in paired comparison systems

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  • Maria Bolsinova
  • Gunter Maris
  • Abe D. Hofman
  • Han L. J. van der Maas
  • Matthieu J. S. Brinkhuis

Abstract

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

Suggested Citation

  • Maria Bolsinova & Gunter Maris & Abe D. Hofman & Han L. J. van der Maas & Matthieu J. S. Brinkhuis, 2022. "Urnings: A new method for tracking dynamically changing parameters in paired comparison systems," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(1), pages 91-118, January.
    • Handle: RePEc:bla:jorssc:v:71:y:2022:i:1:p:91-118
    DOI: 10.1111/rssc.12523
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    References listed on IDEAS

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    1. Lehmann, Robert & Wohlrabe, Klaus, 2017. "Who is the ‘Journal Grand Master’? A new ranking based on the Elo rating system," Journal of Informetrics, Elsevier, vol. 11(3), pages 800-809.
    2. Mark Glickman, 2001. "Dynamic paired comparison models with stochastic variances," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(6), pages 673-689.
    3. Hvattum, Lars Magnus & Arntzen, Halvard, 2010. "Using ELO ratings for match result prediction in association football," International Journal of Forecasting, Elsevier, vol. 26(3), pages 460-470, July.
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