On Iverson’s law of similarity
Journal
Journal of Mathematical Psychology
Journal Volume
127
Start Page
102943
ISSN
0022-2496
Date Issued
2025-12
Author(s)
Abstract
Iverson (2006b) proposed the law of similarity ξs(λx)=γ(λ,s)ξη(λ,s)(x)for the sensitivity functions ξs(s∈S). Compared to the former models, the generality of this one lies in that here γ and η can also depend on the variables λ and s. In the literature, this model (or its special cases) is usually considered together with a given psychophysical representation (e.g. Fechnerian, subtractive, or affine). Our goal, however, is to study at first Iverson's law of similarity on its own. We show that if certain mild assumptions are fulfilled, then ξ can be written in a rather simple form containing only one-variable functions. The obtained form proves to be very useful when we assume some kind of representation. Motivated by Hsu and Iverson (2016), we then study the above model assuming that the mapping η is multiplicatively translational. First, we show how these mappings can be characterized. Later we turn to the examination of Falmagne's power law. According to our results, the corresponding function ξ can have a Fechnerian representation, and also it can have a subtractive representation. We close the paper with the study of the shift invariance property.
Subjects
Fechnerian representation
Iverson's law of similarity
Psychophysical function
Sensitivity function
Subtractive representation
Publisher
Elsevier BV
Type
journal article