We present a probabilistic observer model that accounts for this perceptual behavior. Specifically, we adopt the general hypothesis that the brain attempts to perform optimal estimation of stimulus parameters based on noisy sensory evidence and prior expectations. However, we augment this hypothesis by assuming that the observer performs the secondary estimation task in the belief that his/her previous decision regarding the data was correct. Noisy sensory evidence may initially support both decisions, although with different probability. After making the decision, however, the observer discards all potential estimates that are not in agreement with the choice. This leads to the observed repulsive bias away from the decision boundary. The model fits the data well and makes quantitative predictions for novel experiments.

It is worth noting that the behavior of the model is suboptimal in terms of estimation performance. An optimal (Bayesian) observer model would compute estimates from the sensory evidence under each possible decision taken, and then average these estimates, weighting each according to the probability that the corresponding decision is correct. Thus, our model implies that humans sacrifice performance in order to maintain self-consistency.