On cross-modal commutativity in magnitude production for loudness and brightness

Can the loudness of a tone be compared to the brightness of a light? The answer is affirmative. We appear to be intuitively capable of making such cross-modal comparisons. Psychophysical research has long assumed that these comparisons are mediated by a common scale of subjective intensity shared across modalities. R.D. Luce (2002, Psychological Review, 109, 520-523) developed a psychophysical theory of magnitude estimation and production based on this assumption and derived empirically testable conditions. In particular, he identified cross-modal commutativity as a key property for empirically evaluating the theory. In an extended, high-powered replication of an experiment reported by W. Ellermeier, F. Kattner, and A. Raum (2021, Attention, Perception, & Psychophysics, 83, 2955-2967), the present study examined this property using a cross-modal magnitude production task for loudness and brightness. Relative to the previous study, individual-level analyses yielded more substantial evidence both for and against crossmodal commutativity, while group-level results remained inconclusive. These findings are discussed in light of a generalized theory that predicts a near-miss to cross-modal commutativity while preserving the assumption of a shared representation of subjective intensity.