Robust averaging during perceptual judgment is not optimal.

de Gardelle and Summerfield (1) claimed that, when judging the mean of a set of stimuli, it is optimal to downweight outliers, and that human subjects follow this robust averaging strategy. Here, we show that, in their task, the optimal observer would equally weight all observations. In ref. 1, subjects were presented with a set of eight colors that are denoted by a vector x = (x 1 ,. . ., x 8) and drawn independently from a Gaussian distribution on a red– blue color axis with variance σ 2 and mean of either μ (blue) or −μ (red). On a given trial, μ was set randomly to one of two values, and σ 2 was set randomly to one of three values. The subject indicated whether the mean was blue (C = 1) or red (C = −1). When the prior probabilities are equal, the optimal decision is based on the likelihoods of both options [i.e., p(x | C = 1) and p(x | C=−1)]. Because μ and σ 2 are unknown to the observer, the optimal observer computes these likelihoods by averaging (marginalizing) over all six possibilities (Eq.