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Steingrimsson (Attention, Perception, &amp; Psychophysics, 71, 1916-1930, 2009) outlined Luce's (Psychological Review, 109, 520-532 2002, 111, 446-454 2004) proposed psychophysical theory and tested, for brightness, behavioral properties that, separately, gave rise to two psychophysical functions, Ψ (⊕) and [Formula: see text]. The function Ψ (⊕) maps pairs of physical intensities onto positive real numbers and represents subjective summation, and the function [Formula: see text] represents a form of ratio production. This article, the second in a series expected to consist of three articles, tests the properties linking summation and production such that it forces [Formula: see text]. The properties tested are a form of distributivity and, in three experiments, were subjected to an empirical evaluation. Considerable support is provided for the existence of a single function Ψ for both summation and ratio production. The scope of this series of articles is to establish the theory as a descriptive model of binocular brightness perception.

Evaluating a model of global psychophysical judgments for brightness: II. Behavioral properties linking summations and productions