On fallacies and normative reasoning: when people's judgements follow probability theory

The systematic conjunction and disjunction fallacies seen in people’s probability judgments appear to show that people do not reason according to the rules of probability theory. In an experiment examining people’s judgments of the probability of different medical conditions, we find evidence against this view. In this experiment people’s probability judgments closely followed the fundamental ‘addition rule’ of probability theory. This close match to probability theory comes alongside frequent occurrence of the conjunction and disjunction fallacies in those same probability judgments. These results support a model where people reason about probability via probability theory but are subject to random variation or noise in the recall of items from memory. In this model the effect of random variation is cancelled out by the mathematical form of the addition rule, producing agreement with probability theory; however, noise is not cancelled out for conjunctive or disjunctive comparisons, producing conjunction and disjunction fallacy responses.