This paper is a follow-up to Ellermeier, Kattner, and Raum (2021, Attention, Perception, & Psychophysics, 83, 2955–2967), and provides a reanalysis of their data on cross-modal commutativity from a Bayesian perspective, and a theory-based analysis grounded on a recently suggested extension of a global psychophysical approach to cross-modal judgments (Heller, 2021, Psychological Review, 128, 509-524). This theory assumes that stimuli are judged against respondent-generated internal references that are modality-specific and potentially role-dependent (i.e., sensitive to whether they pertain to the standard or the variable stimulus in the performed cross-modal magnitude production task). While the Bayesian tests turn out to be inconclusive, the theory-based analysis reveals a massive and systematic role-dependence of internal references. This leads to predicting small but systematic deviations from cross-modal commutativity, which are in line with the observed data. In analogy to a term coined in the context of Weber’s law, this phenomenon is referred to as near-miss to cross-modal commutativity. The presented theory offers a psychological rationale explaining this phenomenon, and opens up an innovative approach to studying cross-modal perception.
