Evaluating the capacity of paired comparison methods to aggregate rankings of separate groups

Cent Eur J Oper Res. 2023 Feb 12:1-21. doi: 10.1007/s10100-023-00839-3. Online ahead of print.

Abstract

Ranking and rating methods have outstanding significance in sports, mainly due to their capacity to predict results. In this paper we turn to their capacity to aggregate separate groups' rankings based on a small piece of information. We investigate under which conditions two or more separate groups can be trustworthily interwoven applying Thurstone motivated methods and an AHP based method. A theorem is proved which guarantees adequate unified ranking based on some links between the groups. We also analyse the robustness of the results.

Keywords: AHP; Aggregation; Bradley–Terry model; Evaluation of sports tournaments; Maximum likelihood estimation; Paired comparison; Thurstone method; Weighted LLSM.