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Conjunction Probability Error
The conjunction rule applies to predictive judgment or forward conditional reasoning. It is a normative rule that states that the probability of any combination of events cannot exceed the probability of constituent events. For example, the probability of picking the queen of spades from a card deck cannot exceed the probability of picking a spade and a queen from the deck. Typically, people can successfully apply the conjunction rule to transparent problems such as the card selection problem. However, there is overwhelming evidence that when problems are less transparent, people often ignore the rule and judge the conjunction of events as more probable than a constituent event, thereby committing the conjunction probability error. Because of the pervasiveness of the conjunction error and its clear violation of normative probability theory, it is important to understand conditions that tend to produce the error, procedures that may reduce its occurrence, and instances where it does not apply.
Conditions That Produce the Conjunction Error
The initial investigation of the conjunction error was conducted within the framework of understanding how heuristic thought processes may produce systematic biases in judgment and choice. In their seminal investigation, Amos Tversky and Daniel Kahneman first explored the conjunction error as resulting from the use of the representativeness heuristic for judging probabilities. According to this heuristic, people judge probabilities for specific outcomes by making a similarity comparison with a model of the population from which the outcomes were sampled. For example, knowing that a person is a member of a particular group, one may use a stereotype of that group as a model to predict behaviors or attributes of the person.
The Linda Problem
An often used example that has been shown to produce robust conjunction errors is the Linda problem. As described by Tversky and Kahneman, Linda is 31 years old, single, outspoken, and intelligent. Participants are told that when she was a philosophy major at school, she was concerned with social justice and participated in protests and demonstrations. This background establishes a model of Linda as a sophisticated individual concerned with social issues. After reading the description, participants typically rank the relative likelihoods of predicted occupations and activities that apply to Linda. Three key statements that may be evaluated include the following:
The first statement is unlikely (U) based on the model of Linda and is given a relatively low probability ranking. The second statement is likely (L) based on the model of Linda and is given a relatively high probability ranking. The third statement is the key statement as it conjoins the unlikely and likely events (U & L). As such, it represents a subset of both these events and cannot have a higher probability than either of these. Yet nearly all participants indicate that the conjunction is more probable than the unlikely event. These results are obtained with both statistically naive and statistically sophisticated participants and in situations in which participants are directly assessing the relative likelihoods of the events. Furthermore, a majority of participants still commit the error even when they are asked to bet on these outcomes, implying the effect does not disappear with monetary incentives for correct application of the conjunction rule.
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