Bayesian estimation yields anti-Weber variability

A classic result of psychophysics is that human perceptual estimates are more variable for larger magnitudes. This "Weber behavior," however, has typically not been the focus of the prominent Bayesian paradigm. Here, we examine the variability of a Bayesian observer in comparison with human subjects. In two preregistered experiments, we manipulate the prior distribution and the reward function in a numerosity-estimation task. When large numerosities are more frequent or more rewarding, the Bayesian observer exhibits an "anti-Weber behavior," in which larger magnitudes yield less variable responses. Human subjects exhibit a similar pattern, thus breaking a long-standing result of psychophysics. Nevertheless, subjects' responses are best reproduced by a logarithmic encoding of magnitudes, a proposal of Fechner often regarded as accounting for Weber behavior. We thus obtain an anti-Weber behavior together with a Fechner encoding. Our results suggest that the increasing variability may be primarily due to the skewness of natural priors.