Statistical inference for pairwise comparison models

Pairwise comparison involves assessing subjects in pairs to establish their relative preferences, a concept relevant to numerous applications such as sports analytics [13, 20, 30], econometrics [23], video coding [19], and social science [22], to name just a few. A prevalent method for pairwise comparison modeling employs a latent score framework. Originated from the ideas in Thurstone [29] and Zermelo [33], a mathematical model for pairwise comparison data analysis was proposed in the work by Bradley and Terry [4]. Subsequent developments led to multiple generalizations, including ordinal models such as the Rao-Kupper model [26] and the Davidson model [10], which account for ties, the cumulative link model [1] that considers more refined ordinal scales, and cardinal models such as the paired cardinal model [27]. We recommend [5] for a review of the related topics in pairwise comparison modeling. Given the growing number of subjects in the big-data era, recent research trends focus on understanding the asymptotic behavior of estimating the latent score vector as the number of compared subjects approaches infinity.