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

Abstract

Steingrimsson (Attention, Perception, & 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 Ψ{ring operator}p. The function Ψ⊕ maps pairs of physical intensities onto positive real numbers and represents subjective summation, and the function Ψ{ring operator}p 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 Ψ{ring operator}p = Ψ⊕ = Ψ. 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. © The Author(s) 2010.