Tversky and Kahneman’s (1983) classic exposition of the conjunction fal-lacy is essential reading for anyone interested in the phenomenon. Yates and Carlson’s (1986) influential paper served to demonstrate the highly contin-gent nature of the fallacy, and Wolford, Taylor, and Beck’s (1990) critique is relevant not only in terms of its relevance to the present chapter but also to the broader debate on human rationality. In this regard, Stanovich and West’s (2000) account of the debate both in terms of the conjunction fallacy and more generally makes fascinating reading.
NOTES
1 The conjunction of two events is defined as: P(A&B) = P(A) × P(B|A). Since prob-abilities cannot exceed 1 then P(B|A) ≤ 1; therefore P(A) × P(B|A) ≤ P(A) and so P(A&B)≤ P(A). The same reasoning holds for P(B).
2 Hertwig and Chase describe this outcome in terms of the application of a “ceiling rule” and we shall return to their conceptualization later in the chapter.
3 Until my recent paper (Fisk, 2002), Shackle’s theory had not been subjected to direct empirical investigation.
4 Given a positive conditional relationship and given that event A is more surprising than event B, such that y0A < yB < yA, then the conjunctive surprise value will be based on yB (the larger of y0A and yB). With no conditional relationship then yB < yA
= y0A and the surprise value of the conjunction will be based on yA (the larger of yA and yB). Thus the positive conditional relationship shifts the focus for the con-junctive judgement from the more surprising to the less surprising event, but under most circumstances the actual magnitude of the positive conditional relationship has no direct impact on the conjunctive value.
5 Given the multiplicative nature of the normative relationship, a 0.1 change in the smaller component event probability will produce a larger change in the conjunctive probability than a 0.1 change in the larger component event.
6 In fact, multiplying the component probabilities together to obtain the conjunctive probability is only normative for independent events. Tversky and Kahneman note
that many participants perceive a negative conditional relationship between the two component events in the Linda scenario.
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