Analyizing the Conjunction Fallacy as a Fact

TL;DR

The paper reframes the conjunction fallacy (CF) as a problem of extensional probability rather than solely an explanatory bias, by analyzing the feasible space of the probability triple $(P(A),P(B),P(AB))$ within $[0,1]^3$ and examining how often real data occupy this space. Through a literature review spanning 1983–2016, it shows that empirical data cover only a narrow region of the extensional space, with sparse sampling in several regions and a predominance of single-CF cases over no-CF or double-CF configurations. It argues that Boole's conditions of possible experience constrain which points are feasible, and that many influential accounts rely on more limited data reporting, hindering cross-study comparisons. The authors advocate using factual paradigms that directly measure $(P(A),P(B),P(AB))$ across the full extensional space to better understand CF, test rationalist versus non-rational accounts, and potentially incorporate non-classical perspectives.

Abstract

Since the seminal paper by Tversky and Kahneman, the conjunction fallacy has been the subject of multiple debates and become a fundamental challenge for cognitive theories in decision-making. In this article, we take a rather uncommon perspective on this phenomenon. Instead of trying to explain the nature or causes of the conjunction fallacy (intensional definition), we analyze its range of factual possibilities (extensional definition). We show that the majority of research on the conjunction fallacy, according to our sample of experiments reviewed which covers literature between 1983 and 2016, has focused on a narrow part of the a priori factual possibilities, implying that explanations of the conjunction fallacy are fundamentally biased by the short scope of possibilities explored. The latter is a rather curious aspect of the research evolution in the conjunction fallacy considering that the very nature of it is motivated by extensional considerations.

Figures (2)

• Figure 1: Examples of two data points, one not committing the fallacy ($NF$) and another committing it ($F$). Note that for $NF$, the projections of the vector onto the $P(A)$ and $P(B)$ axes are larger than the projection onto the axis $P(AB)$, while the opposite is true for $F$
• Figure 2: CF data reported and coloured by the extent fallacy violation. Green means no violation, blue means violation on one of the probabilities, and red means violation on two of the probabilities.