The Bat-and-Ball Problem: Stronger evidence in support of a conscious error process

Abstract

Traditional accounts of reasoning have characterized human error response to be an unconscious process whereby cognitive misers blindly neglect the critical information that would lead to problem solution, thereby substituting an easier problem for the actual problem (e.g., Kahneman & Frederick, 2002). For the bat-and-ball problem, the unconscious substitution hypothesis is challenged on two fronts in the present study: (1) testing for conscious representation of the error-inducing semantic content of the problem (i.e., the "more than" phrase, "The bat costs $1.00 more than the ball."); and (2) comparing experimentally response confidence differences between standard versions of the problem and isomorphic controls (without that phrase) to verify post-decision sensitivity to the errors, following De Neys, Rossi, and Houdé (2013). Crucially, even when interference questions were included between testing and memory response, incorrect reasoners largely had accurate recall and recognition of the problem's error inducing phrase. Incorrect reasoners' intra-individual error sensitivity was replicated and extended via the introduction of a social-metacognitive measurement, which was found to be correlated with intra-individual post-decision confidence and also yielded an error sensitivity effect. Finally, latency responses verify the relationship between time spent reasoning and post-decision confidence. Implications and future directions are discussed.

Keywords: attribute substitution; bat-and-ball problem; confidence; decision-making; error sensitivity; latency response; memory; reasoning.

Figure 1

Response confidence scores (top panel) and opinion judgment scores (bottom panel) (in proportions) for standard and control variants of the bat-and-ball problem by reasoners incorrect and correct on the standard question. Note that the scale on the vertical axis differs in the two panels. The error bars represent standard errors of the mean.