Investigating the symmetry of human probability judgment biases

People’s probability judgments are both biased and variable. When asked to judge the probability of binary events, e.g., whether it will rain or not, there is a bias away from extreme values. In addition, there is substantial variability when judgments of the same question are repeated, even when no new information has been presented. This combination of bias and variability has been best explained by sampling-based models. Variability is neatly explained by people basing their probability judgments on randomly recalled or simulated events. Bias though is not an inherent property of random samples, so bias is introduced through noisy counting of samples (e.g., Probability Theory Plus Noise; Costello & Watts, 2014) or by application of a generic prior over probabilities themselves to improve judgment accuracy for small numbers of samples (e.g., Bayesian Sampler; Zhu, Sanborn, & Chater, 2020). These two mechanisms make equivalent predictions for average judgments but are distinguished by their predictions for the relationship between the judgment mean and variance. Using, a recent regression-based technique, Sundh, Zhu, Chater, and Sanborn (in press) found empirical evidence for a generic prior. But the flexibility of the prior was not tested – can it adapt, particularly to environments in which probabilities are not symmetrically distributed (e.g., there are more small, or large, probabilities).? Here we expand the regression-based technique to allow it to identify either symmetric or asymmetric generic priors. Applied to four previous experiments in which participants make repeated probability judgments, the recovered generic prior was close to symmetric. These previous experiments however asked participants to judge event distributions that were themselves symmetric, so to provide a better test, we ran two new experiments in which the distribution of probabilities to judge were asymmetric. We again found that the prior was close to symmetric, suggesting that perhaps the mind has symmetry constraints, the generic prior reflects long-term experience, or that the generic prior is not represented at all but implemented “procedurally” by fixed a process of regression to the mean.