Why the Conjunction Effect Is Rarely a Fallacy: How Learning Influences Uncertainty and the Conjunction Rule

Abstract

In this article we explore the relationship between learning and the conjunction fallacy. The interpretation of the conjunction effect as a fallacy assumes that all observers share the same knowledge, and that nobody has access to privileged information. Such situations are actually quite rare in everyday life. Building on an existing model of surprise, we prove formally that in the more typical scenarios, where observers are alert to the possibility of learning from event outcomes, the conjunction rule does not apply. Scenarios which have been engineered to produce the so-called conjunction “fallacy” (e.g., Tverksy and Kahneman, 1983) often imply subjective uncertainty and hence the possibility of learning. In Experiment 1 we demonstrate that when these scenarios are rephrased so as to eliminate subjective uncertainty, the effect is mitigated. In Experiment 2 we demonstrate that when subjective uncertainty is reduced by allowing participants to learn about the mechanism behind a conjunction-inducing scenario, the conjunction effect again diminishes. We conclude that the conjunction effect arises due to the unnaturalness of interpreting verbal descriptions in terms of a situation in which all observers share the same knowledge. Instead, when people hear descriptions of real world situations, they are likely to assume that learning is possible, and that subjective rather than objective uncertainty applies.

Scalar implicatures under uncertainty

“…In this design, the relative amount of conjunction errors was significantly reduced (Hertwig and Gigerenzer, 1999;Fiedler, 1988) Gigerenzer argues that the conjunction error is reduced in a frequency format because individuals tend to represent probabilistic information in terms of frequencies (Gigerenzer, 1994). This is further supported by more recent work which demonstrated that when the Linda Problem is framed as a query search for a computer database, where the description is framed as a set of parameters (e.g., age = 31, college major = philosophy) conjunction errors are yet again reduced (Maguire et al, 2018). Table 4.1 summarizes key experimental manipulations and their relative incidence of conjunctive errors.…”