One of the central assumptions of mainstream economics has been that people make rational choices. As a challenge to this assumption, Nobel prize winning behavioural economist Prof. Daniel Kahneman gives an example where some Americans were offered a choice of insurance against their own death in a terrorist attack while on a trip to Europe, or insurance that would cover death of any kind on the trip. People were willing to pay more for the former insurance, even though ‘death of any kind’ includes ‘death in a terrorist attack’.
This is an instance of the Conjunction Fallacy, which is based on the false assumption that specific conditions are more probable than general ones. This fallacy usually stems from thinking the choices are alternatives, rather than members of the same set.
The logical form of this fallacy is:
Premise: X is a subset of Y.
Conclusion: Therefore, X is more probable than Y.
The probability of a conjunction is never greater than the probability of its conjuncts. In other words, the probability of two things being true can never be greater than the probability of one of them being true, since in order for both to be true, each must be true. However, when people are asked to compare the probabilities of a conjunction and one of its conjuncts, they sometimes judge that the conjunction is more likely than one of its conjuncts. This seems to happen when the conjunction suggests a scenario that is more easily imagined than the conjunct alone.
Interestingly, Kahneman discovered in earlier experiments that statistical sophistication made little difference in the rates at which people committed the conjunction fallacy. This suggests that it is not enough to teach probability theory alone, but that people need to learn directly about the conjunction fallacy in order to counteract the strong psychological effect of imaginability.