Internal References in Cross-Modal Judgments: A Global Psychophysical Perspective

We are able to compare intensities across different sorts of stimuli, like in matching the brightness of visual stimuli of different hue, or the loudness of auditory stimuli of different spectral shapes. We can even match the brightness of a visual stimulus to the loudness of a tone, and vice versa. The termcross-dimensional matching is used to subsume these kinds of intra- and cross-modal tasks. The often replicated regression effect in cross-dimensional matching relates to the observation that the intensity of whatever stimulus is adjusted exhibits a tendency toward some mean magnitude, which is interpreted as serving as an internal reference. Internal references, however, are not part of psychophysical theory in the tradition of Stevens. They form a key ingredient for the theory of global psychophysics initiated by R. Duncan Luce, which also makes explicit Stevens' assumption of an underlying ratio scale of perceived intensity to which all sensations map, and renders it empirically testable. The present article generalizes Luce's theory of cross-dimensional magnitude production (Luce et al., 2010) to integrate potentially role-dependent internal references (pertaining to the standard, or the adjusted stimulus) as suggested by the regression effect. Reconsidering available empirical evidence for magnitude production and matching experiments in the light of these theoretical developments leads to a coherent picture. The results indicate that internal references are role-dependent in cross-dimensional tasks (intra- or cross-modal), but role-independent in intra-dimensional tasks. Moreover, predictions derived from the generalized theory provide a close fit to classical matching data.