Additive or Multiplicative Perceptual Noise? Two Equivalent Forms of the ANCHOR Model

ANCHOR is an integrated memory-based scaling model that accounts for a wide range of phenomena in category rating and absolute identification. The model uses anchors stored in memory that serve as prototypes for each response category. The stimuli are represented by magnitudes. Two alternative formulations of the magnitude variability are considered: additive noise, which leads to logarithmic scales, and multiplicative noise, which leads to power scales. Both formulations are consistent with Weber’s and Stevens’s laws. Four variants of the ANCHOR framework systematically explore these alternative formulations. The performance of the models is evaluated against experimental data. The results show that the form of the perceptual equation is not critical for the operation of the model. Thus, the power vs. logarithmic controversy does not affect ANCHOR’s central claim that human scaling performance is memory-based.