About cross-modal commutativity in magnitude production

Can we compare the loudness of a tone to the brightness of a light? The answer is yes. We are intuitively capable of these cross-modal comparisons. Psychophysical researchers such as Stevens have long assumed that these cross-modal comparisons are mediated by a single scale of subjective intensity. Luce (2002) developed a psychophysical theory for physical intensity making Stevens’ assumptions towards an underlying scale of perceived intensity explicit and formulating empirically testable conditions for it. They identified cross-modal commutativity as a property through which the theory can be tested. We investigated this property in a cross-modal magnitude production task between auditory and visual stimuli, concerning their loudness and brightness respectively. Participants were presented with the two stimuli and instructed to, for example “make the tone 3 times as loud [as the visual stimuli appears bright]”. This was partly a replication of Ellermeier et al. (2021). They concluded that cross- modal commutativity holds whereas we find inconclusive evidence in a Bayesian analysis. More importantly, in a theoretical analysis, we find evidence that role-independence of the internal references used in magnitude production is violated. In an expansion of Luce’s theory, Heller (2021) concluded that cross- modal commutativity holds if and only if the internal references are role-independent, meaning they are not dependent on whether the reference pertains to the standard or the variable stimulus. This means, if role-independence of the internal references is violated, the assumed intensity scale can hold even if cross- modal commutativity doesn't. Evidence towards this conclusion as well as its implications will be discussed.