Cross-modal and intra-modal commutativity of magnitude productions

Luce, Steingrimsson, and Narens (Psychological Review, 117, 1247-1258, 2010) postulated that if ratio magnitude productions involving two perceptual dimensions exhibit "cross-dimensional commutativity," they may be represented on a single internal scale of subjective intensity. Commutativity here refers to the order independence of successive magnitude productions (e.g., adjusting the subjective intensity of a stimulus successively by factors of 2 and 3 should produce the same result regardless of which factor comes first [×2×3 = ×3×2]). In the present experiment, these operations were performed (1) within the same modality (here: loudness or brightness), and (2) across modalities-that is, making productions from light to sound (e.g., "make the sound twice as loud as the light is bright") and back, or vice versa. In individual, within-subjects experiments involving repeated loudness and brightness productions, 13 participants made adjustments to evaluate both kinds of commutativity. In line with previous findings (Ellermeier, Kattner, & Raum, Attention, Perception, & Psychophysics, 83[7], 2955-2967, 2021), both intra-modal and cross-modal commutativity held for most participants, but the final results of corresponding sequences of cross-modal and intra-modal adjustments (e.g., of the type ×2×3) typically did not coincide. That inconsistency is interpreted as participants choosing different internal reference points when making cross-modal versus intra-modal magnitude productions, but it does not preclude their using a common internal yardstick. The aggregated and raw data of all participants are available in an OSF repository ( https://osf.io/5avbw/?view_only=687aef266f174648863f86b4982e35b9 ). The study has not been preregistered.