A power law is a relationship in which a relative change in one quantity, like length of side in a square, gives rise to a proportional relative change in another quantity (area), independent of the initial size of those quantities. This idea pops up across so many different domains from size of cities according to population, to word frequencies across languages, to learning (and forgetting!).
One power law in particular, Weber’s law, has historically been important for describing people’s perception of stimuli. Weber’s law describes the tendency of our perceptual systems to utilize relative rather than absolute differences to discriminate between stimuli. Think trying to discriminate between bowling balls. If you pick up a 16-pound ball in one hand and an 8-pound ball in another, you’re going to notice the difference. But trying to discriminate between a 16-pound ball and a 15-pound ball is going to be much tougher.
Jeff Gassen of Texas Christian University wanted to look at whether Weber’s law had any implications for the processes that shape our mate choices and perception of facial attractiveness. In a series of studies, Gassen morphed three pairs of faces in 10% increments of attractiveness (as rated by other participants in previous studies) and had participants choose which was more attractive in order to measure whether participants’ choices were better predicted by absolute or relative differences between the faces.
Lo and behold, facial preferences were much better predicted by relative differences between the faces as opposed to actual differences. Think comparing someone who people describe as a “3/10” to another person who is a “5/10”. You can feel the difference in attractiveness between those two is way more obvious than the difference between someone who’s an “8/10” and someone who is a “10/10.” Gassen found this relationship held even when they used eye-tracking as a measure of interest.
Our decisions about facial attractiveness (and other comparisons of complex stimuli) are influenced by power law, accoridng to this research. When we compare faces, we’re not analyzing exact differences, but rather how the faces stack up next to each other. These scaling relationships can be tricky to grasp but are found everywhere. If you take anything from this, dear reader, let it be that beauty is in the brain of the beholder!
Written By: Erika Pages, PhD Candidate at Arizona State University
Session: “Beauty is in the Psychophysics of the Beholder: Facial Attractiveness, Sexual Selection, and Weber’s Law”, a talk presented at the Student/Early Career Data Blitz 2, held on February 29th, 2020
Speakers: Jeff Gassen, Texas Christian University