Surprisingly Rational: Evidence that people follow probability theory when judging probabilities, and that biases in judgment are due to noise

The systematic biases and errors seen in people's probability judgments are typically taken as evidence that people do not reason about probability using the rules of probability theory. We show the contrary: that these biases are a consequence of people correctly following probability theory, but with random variation or noise affecting the reasoning process. Taking P_E(A) to represent a person's estimate for the probability of some event A, this random variation account predicts that on average P_E(A)+P_E(B)- P_E(A or B)-P_E(A and B)=0 for all pairs of events A,B, just as required by probability theory. Analysing data from an experiment asking people to estimate such probabilities for a number of pairs A,B we find striking confirmation of this prediction.