Evaluating a model of global psychophysical judgments-I: Behavioral properties of summations and productions

The research presented is a partial empirical evaluation of the second author's proposed psychophysical theory [Luce (2002). Psychological Review, 109, 520-532; Luce (2004). Psychological Review, 111, 446-454]. The theory deals with the global percept of subjective intensity, in which there is a psychophysical function Ψ that maps pairs of physical intensities onto the positive real numbers and represents, in an explicit mathematical way, subjective summation and a form of ratio production. A number of behavioral properties have been shown to follow from these specific representations, and in the presence of certain plausible background assumptions these properties are also sufficient for the representations. In four auditory experiments, key behavioral properties of summation over the two ears and a form of generalized ratio production are evaluated empirically. Considerable support is reported for particular forms of Ψ for summations and ratio productions separately. A second article, Steingrimsson and Luce (Journal of Mathematical Psychology, in press), explores the behavioral properties that link summations and productions.