I recently gave a talk on the conditional probabilities of unique events (Khemlani, Lotstein, & Johnson-Laird, 2014) at the 8th London Reasoning Workshop at Birkbeck College. You can download the presentation here.
Here’s the abstract:
We describe a dual-process theory of how individuals estimate the probabilities of unique events, such as Hillary Clinton becoming US President. It postulates that uncertainty is a guide to improbability. In its computer implementation, an intuitive system 1 simulates evidence in mental models, and forms analog non-numerical representations of the magnitude of degrees of belief. This system has minimal computational power, and combines evidence using a small repertoire of primitive operations. It resolves the uncertainty of divergent evidence for single events and for conjunctions and disjunctions of events by taking a primitive average of non-numerical probabilities. It computes conditional probabilities in a tractable way, treating the given event as evidence that may be relevant to the probability of the dependent event. We report an experiment on conditional probabilities that corroborated the theory’s predictions. Participants concurred in estimates of real possibilities. They violated the complete joint probability distribution in the predicted ways. They were faster to estimate the probabilities of compound propositions when they had already estimated the probabilities of each of their components. We discuss the implications of these results for theories of probabilistic reasoning.