Smith (2015) describes an explosion of interest in Benford’s law, that for data from many domains the first digits have a log distribution. Few studies have similarly asked whether the numbers people generate fit to Benford’s law, but recent data show a reasonable fit. This paper argues that testing for fit to Benford’s law is the wrong question for behavioural data, instead we should think in terms of a “Benford bias” in which the first-digit distribution is distorted towards Benford’s law. We propose calculating the effect size of this bias by testing a linear contrast weighted by Benford’s law. Analyses of existing data sets yielded effect sizes of 0.43-0.52. Applying this approach to a new task extended the scope of Benford bias to predicting outputs of a linear system and found an effect size of .40. Benford bias may be a ubiquitous influence on judgments and decisions based on numbers.

The Monty Hall Dilemma (MHD) is a well-known cognitive illusion. It is often claimed that one reason for the incorrect answers is that people apply the equiprobability principle: they assume that the probability of the two remaining options must be equal. An alternative explanation for assigning the same probabilities to options is that they had the same prior probabilities and people perceive no significant change. Standard MHD versions do not distinguish these possibilities, but a version with unequal prior probabilities could. Participants were given an unequal probabilities version of MHD and told that either the high or low probability option had been eliminated. This affected participants’ choices and their posterior probabilities. Only 14% of participants’ responses were consistent with applying the equiprobability principle, but 51% were consistent with a “no change” principle. Participants were sensitive to the implications of the prior probabilities but did not appear to use Bayesian updating.