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

Steingrimsson and Luce [Journal of Mathematical Psychology, in press] outlined the second author's proposed psychophysical theory [Luce (2002), Psychological Review, 109, 520-532; Luce (2004a) Psychological Review, 111, 446-454] and tested behavioral attributes that, separately, gave rise to two psychophysical functions, Ψ⊕ and Ψ∘p. The function Ψ⊕ maps pairs of physical intensities onto the positive real numbers and represents subjective summation, and the function Ψ∘p represents a form of ratio production. This article evaluates properties linking summation and production in such a way as to force Ψ∘p=Ψ⊕=Ψ. These properties, which are a form of distributivity, are subjected to an empirical evaluation in three experiments. The testing strategy is carried out in the auditory domain and concerns the subjective perception of loudness. Considerable support is provided for the existence of a single function Ψ for both summation and ratio production.