Bronx Baseball Bat & Ball Set

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Scherer LD, Yates JF, Baker SG, & Valentine KD (2017). The influence of effortful thought and cognitive proficiencies on the conjunction fallacy: Implications for dual-process theories of reasoning and judgment. Personality and Social Psychology Bulletin, 43, 874–887. doi: 10.1177/0146167217700607 [ PubMed] [ CrossRef] [ Google Scholar]

Lichtenstein S, & Fischhoff B (1977). Do those who know more also know more about how much they know? Organizational Behavior and Human Performance, 20, 159–183. doi: 10.1016/0030-5073(77)90001-0 [ CrossRef] [ Google Scholar] Szollosi A, Bago B, Szaszi B, & Aczel B (2017). Exploring the determinants of confidence in the bat-and-ball problem. Acta Psychologica, 180, 1–7. doi: 10.1016/j.actpsy.2017.08.003 [ PubMed] [ CrossRef] [ Google Scholar] System 2 thinking, on the other hand, is slow, rational, reflective, and effortful. It gets into the driver’s seat when you focus and concentrate on a complicated problem. As for the response confidence scores, the opinion judgments are reported here as proportions rather than percentages. There was a positive relationship between standard question confidence and standard question opinion judgments for incorrect reasoners, r(225) = .480, p< .001, such that incorrect reasoners who were less confident in their response were also less likely to think other reasoners could answer the standard question correctly. This strong relationship lends support to the notion that opinion judgments and response confidence scores are reflecting similar cognitive processes.Bourgeois-Gironde S, & Vanderhenst J-B (2009). How to open the door to System 2: Debiasing the Bat and Ball problem. In Watanabe S, Bloisdell AP, Huber L, & Young A (Eds.), Rational animals, irrational humans (pp. 235–252). Tokyo: Keio University Press. [ Google Scholar] Mata A, & Ferreira MB (2018). Response: Commentary: Seeing the conflict: an attentional account of reasoning errors. Frontiers in Psychology, 9, 24. doi: 10.3389/fpsyg.2018.00024 [ PMC free article] [ PubMed] [ CrossRef] [ Google Scholar] For the recall response, a mixed effects logistic regression (with subject as the random variable) was conducted due to the dichotomous dependent variable (with or without “more than”), considering only those participants who wrote down an answer that could be coded as with or without the “more than” phrase (e.g., “don’t know” responses were excluded). Incorrect reasoners usually recalled the standard problem, but not the control, as containing “more than” (see Table 1), with this effect of condition significant, b = 3.02, odds ratio ( OR) = 20.44, χ 2 = 21.69, p< .001, 95% confidence interval ( CI) [5.74, 72.75]. B. T., & Stanovich KE (2013). Dual-process theories of higher cognition: Advancing the debate. Perspectives on Psychological Science, 8, 223–241. doi: 10.1177/1745691612460685 [ PubMed] [ CrossRef] [ Google Scholar]

De Neys W, Rossi S, & Houdé O (2013). Bats, balls, and substitution sensitivity: Cognitive misers are no happy fools. Psychonomic Bulletin & Review, 20, 269–273. doi: 10.3758/s13423-013-0384-5 [ PubMed] [ CrossRef] [ Google Scholar]The question really belongs more to the science of the mind than it does to mathematics and logic— it is about the assumptions we make, rather than whether or not we have the ability to solve the question.