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Adaptive paired comparison design

Authors
Journal
Journal of Statistical Planning and Inference
0378-3758
Publisher
Elsevier
Publication Date
Volume
127
Identifiers
DOI: 10.1016/j.jspi.2003.09.022
Keywords
  • Bayesian Optimal Design
  • Bradley–Terry Model
  • Competition
  • Swiss System
  • Tournament Schedule
Disciplines
  • Computer Science
  • Design
  • Mathematics

Abstract

Abstract An important aspect of paired comparison experiments is the decision of how to form pairs in advance of collecting data. A weakness of typical paired comparison experimental designs is the difficulty in incorporating prior information, which can be particularly relevant for the design of tournament schedules for players of games and sports. Pairing methods that make use of prior information are often ad hoc algorithms with little or no formal basis. The problem of pairing objects can be formalized as a Bayesian optimal design. Assuming a linear paired comparison model for outcomes, we develop a pairing method that maximizes the expected gain in Kullback–Leibler information from the prior to the posterior distribution. The optimal pairing is determined using a combinatorial optimization method commonly used in graph-theoretic contexts. We discuss the properties of our optimal pairing criterion, and demonstrate our method as an adaptive procedure for pairing objects multiple times. We compare the performance of our method on simulated data against random pairings, and against a system that is currently in use in tournament chess.

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