Fooled by probabilities: developmental trends in superstitious beliefs and numeracy

People persist in confounding random processes with naïve conceptions of chance and luck; at the same time children have early and correct intuitions about probabilities. This research focuses on these developmental inconsistencies under the theoretical background of dual-process theories. Numeracy and superstitious beliefs are investigated in two typical judgment tasks. Words such as chance, luck and probability are terms that people use in everyday life. On the one hand research has shown that adults often make judgments inconsistent with the laws of probability. On the other hand, some studies have shown that 8-10 year olds seem to reason in a more “rational” way than adults in typical judgment tasks. Classical theories of cognitive development cannot explain these counterintuitive findings. Dual-process theories attempt to account for these findings by proposing two distinct systems of reasoning (the analytical and heuristic systems). However, their dissemination within developmental psychology has been limited and the results are mixed. The purpose of this research is to shed light on factors that have led to such inconsistencies. We expect to identify task-specific factors involved in decision making problems that constitute the reason for the present conflicting evidence. Individual beliefs play a role when numerical information and beliefs are in conflict. In Study 1 participants were 90 fifth graders, 99 seventh graders and 153 adults. The if-only task was used varying the superstitious belief (present or absent). No numerical information was provided. In Study 2 participants were 276 fifth graders, 344 seventh graders and 90 adults. The contingency detection problem was used varying: a) probability ratios (equal probability or different probability); b) superstitious belief (present or absent). In Study 1 the age of participants significantly predict whether they gave a heuristic or a normative response. Interestingly, the heuristic responses increased with age, suggesting adults as more prone to the if-only fallacy than children. The superstitious belief did not influence the proportion of heuristic responses. In Study 2 the interaction between the age of participants and the probability ratios was significant. When ratios were equal only fifth graders were influenced by absolute numbers and they focused on the greater number as having a more probable outcome. Instead, when ratios were different, fifth graders gave a higher proportion of correct responses; at the same time the performance of seventh graders and adults decreased. For all the age groups the proportion of atypical responses increased, in particular in adults. This effect was due to the presence of the superstitious belief that influenced the performance paradoxically when the problem is easily solved. These results emphasize the relevance of understanding the developmental trajectory of decision making and these two studies underline the necessity to investigate the task-specific factors that are involved in the interaction between the two systems of reasoning. A specific dual-process account can explain our counterintuitive findings: the Fuzzy-Trace Theory (Brainerd & Reyna, 2001). According to this theory, intuition develops into adulthood and represents an advanced form of mature reasoning. Moreover, results in Study 2 give support to an early development of the interaction between the two systems of reasoning.