On the nature and meaning of sinuosity in magnitude-estimation functions

Magnitude-estimation functions for single observers, derived from multiple judgments of closely spaced stimuli, exhibit a sinuous form in logarithmic coordinates, an observation frequently confirmed since first reported by Luce and Mo (1965). We propose that this can result from reliance on a restricted pool of responses, called preferred numbers by Baird and Noma (1975). We describe a model featuring a response band centered on an assumed power function, from which the observer selects from among preferred numbers with equal probability. In simulations, the expected values of these selections oscillate around the underlying power function with an appearance similar to that of Luce-Mo functions. The appearance of these functions depends on values assumed for the scale factor of the power function, the range of intensities considered, and the width of the band from which responses are drawn. We conclude that sinuosity in magnitude-estimation functions does not disconfirm the psychophysical power law.