Evaluating a Psychophysical Model: Brightness II 1 Running head: EVALUATING A PSYCHOPHYSICAL MODEL: BRIGHTNESS II Evaluating a Model of Global Psychophysical Judgments for Brightness: II. Behavioral Properties Linking Summations and Productions

Steingrimsson (2009) outlined Luce’s (2002, 2004) proposed psychophysical theory and tested, for brightness, behavioral properties 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 tests the properties linking summation and production such that it forces Ψ◦p = Ψ⊕ = Ψ. The properties tested are a form of distributivity and in three experiments are 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 the this series of articles is to establish the theory as a descriptive model of binocular brightness perception.