Component probabilities and the conjunction fallacy: Resolving signed summation and the low component model in a contingent approach

This study investigates the conflicting implications of the low component and signed summation explanations for the conjunction fallacy. Error data across three different conjunction types replicate the pattern found by Yates and Carlson (1986), but the results also reveal, consistent with the predictions of the low component model, that for conjunctions of an unlikely event with a likely event (LU) the unlikely component is given disproportionate weight by subjects. However, this result did not generalise to conjunctions of an unlikely with an unlikely event (UU), nor to those involving a likely with a likely (LL). The combined results show the conjunction fallacy is highly sensitive to task characteristics, and suggests the need for a more contingent explanation of the phenomenon. We argue that the low component model and signed summation are both compatible within a process-based explanation that distinguishes between problem structuring and conjunction evaluation.