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Abstract
Many theorists argue that the probabilities of unique events, even real possibilities such as President Obama's re-election, are meaningless. As a consequence, psychologists have seldom investigated them. We propose a new theory (implemented in a computer program) in which such estimates depend on an intuitive non-numerical system capable only of simple procedures, and a deliberative system that maps intuitions into numbers. The theory predicts that estimates of the probabilities of conjunctions should often tend to split the difference between the probabilities of the two conjuncts. We report two experiments showing that individuals commit such violations of the probability calculus, and corroborating other predictions of the theory, e.g., individuals err in the same way even when they make non-numerical verbal estimates, such as that an event is highly improbable.
Highlights
Everyone from Aristotle to aboriginals engages in probabilistic thinking, even if they know nothing of the probability calculus
We show that naive individuals violate the probability calculus in simple estimates of real possibilities, not just in scenarios contrived to elicit the use of the representativeness of a description as a guide to its probability
We developed a theory based on mental models [10,11] and, unlike previous accounts of the psychology of probabilities, we have implemented the theory in a computer program that yields estimates of the probabilities of unique events
Summary
Everyone from Aristotle to aboriginals engages in probabilistic thinking, even if they know nothing of the probability calculus. The intuitive pre-numerical system yields an analog magnitude monotonically related to the proportion of possibilities in the mental model in which Obama is re-elected We refer to this system as ‘‘pre-numerical’’ because it uses a representation of numbers of the sort that is found in infants [23,24], animals [25], and adults in non-numerate cultures [26], but that continues to exist in adults in Western cultures too [27,28]. If you estimate the chance of Obama’s re-election as 60%, and the chance of an economic recovery in the USA as 40%, you might take 60% of 40%, or vice versa, as your estimate of their joint occurrence Such multiplicative estimates are in accordance with the probability calculus provided that the two events are independent – a condition that the Obama example violates, and so it calls for the computation of P(A) * P(B|A). We carried out several experiments to test these predictions, and report the two most important and representative of them, but their principal results have been replicated in other studies
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