ABSTRACT
Violations of the rules of probability theory and associated systematic reasoning biases have been widely demonstrated. When making judgements concerning uncertain events, individuals frequently produce estimates that are consistently too high, or in other situations consistently too low, or they fail to make use of all of the available information in making judgements about probabilistic events. The focus of the present chapter is conjunctionrule violations. Formally, the conjunction rule may be expressed as follows:
P(A&B) = P(A) × P(B|A) (1)
In simple terms, the probability of event A and event B both occurring together is equal to the probability of event A multiplied by the (conditional) probability of event B given that A has occurred. For example, the probability that I will study (event A) AND pass my exams (event B) is equal to the probability that I will study multiplied by the probability that I will pass GIVEN that I have studied:
P(Study and Pass) = P(Study) × P(Pass | Study) (2)
When the two events A and B are independent then Equation 1 simplifies to
P(A&B) = P(A) × P(B) (3)
since for independent events:
P(B) = P(B|A) = P(B|not A) (4)
The extent to which individuals make judgements consistent with the conjunction rule has been one of the most investigated areas of probabilistic reasoning with research dating back over 40 years (e.g., Cohen, Dearnaley, & Hansel, 1958). More recently the focus of research has shifted to a particular type of violation of the conjunction rule known as the conjunction fallacy (Agnoli & Krantz, 1989; Donovan & Epstein, 1997; Fiedler, 1988;
Fisk, 1996; Fisk & Pidgeon, 1996, 1997, 1998; Gavanski & RoskosEwoldsen, 1991; Tversky & Kahneman, 1983; Wells, 1985; Wolford, Taylor, & Beck, 1990; Yates & Carlson, 1986). The fallacy occurs when the conjunctive probability is assigned a value exceeding that assigned to one or both of the component events, that is,
P(A&B) > P(A) and/or (5)
P(A&B) > P(B). (6)
Such judgements, which violate the conjunction rule,1 are commonplace, with 50-90% of individuals responding in this fashion (Fisk & Pidgeon, 1996; Gavanski & Roskos-Ewoldsen, 1991; Tversky & Kahneman, 1983; Yates & Carlson, 1986).
