The Rating Scale Paradox: Semantics Instability versus Information Loss

Rating systems are applied to a wide variety of different contexts as a tool to map a large amount of information to a symbol, or notch, chosen from a finite, ordered set. Such a set is commonly known as the rating scale, and its elements represent all the different degrees of quality—in some sense—that a given rating system aims to express. This work investigates a simple yet nontrivial paradox in constructing that scale. When the considered quality parameter is continuous, a bijection must exist between a specific partition of its domain and the rating scale. The number of notches and their meanings are commonly defined a priori based on the convenience of the rating system users. However, regarding the partition, the number of subsets and their amplitudes should be chosen a posteriori to minimize the unavoidable information loss due to discretization. Considering the typical case of a creditworthiness rating system based on a logistic regression model, we discuss to what extent this contrast may impact a realistic framework and how a proper rating scale definition may handle it. Indeed, we show that choosing between a priori methods, which privilege the meaning of the rating scale, and a posteriori methods, which minimize information loss, is not strictly necessary. It is possible to mix the two approaches instead, choosing a hybrid criterion tunable according to the rating model’s user needs.