Data in the form of pairwise comparisons arises in many domains, including
preference elicitation, sporting competitions, and peer grading among others.
We consider parametric ordinal models for such pairwise comparison data
involving a latent vector $w^* \in \mathbb{R}^d$ that represents the
"qualities" of the $d$ items being compared; this class of models includes the
two most widely used parametric models--the Bradley-Terry-Luce (BTL) and the
Thurstone models. Working within a standard minimax framework, we provide tight
upper and lower bounds on the optimal error in estimating the quality score
vector $w^*$ under this class of models. The bounds depend on the topology of
the comparison graph induced by the subset of pairs being compared via its
Laplacian spectrum. Thus, in settings where the subset of pairs may be chosen,
our results provide principled guidelines for making this choice. Finally, we
compare these error rates to those under cardinal measurement models and show
that the error rates in the ordinal and cardinal settings have identical
scalings apart from constant pre-factors.

本文考虑使用参数有序模型处理成对比较数据，给出在该模型下最优误差的紧密上下界以及选择两两比较的指导方针，同时与基于基数的测量模型进行比较，结果表明在有序和基数设置下误差率具有相同的比例尺。