Extending the two faces of subjective randomness: From the gambler’s and hot-hand fallacies toward a hierarchy of binary sequence perception

Abstract

In this study, we examined perceptions of binary sequences under uncertainty in an attempt to depict a holistic and unifying framework. The first experiment applied a projection method that motivated participants to observe binary series and provide descriptions of their possible underlying mechanisms or processes. This procedure revealed four distinct perceptual categories: two previously studied categories of chance mechanisms and human performance, associated with the gambler's and hot-hand fallacies, and two newly identified categories-periods and processes and traits and preferences. The next three experiments tested the associations between the four categories and the alternation rates of the observed sequences under three categorical decisions structures: screening, discrimination, and classification. The results reveal the relativity of binary sequence perception. They show that the categories of chance mechanisms and periods and processes reflected rather stable perception across all tested conditions, whereas the other two categories were more susceptible to the context in which they were embedded. The findings support previous research on the gambler's fallacy and show that the hot-hand fallacy is confined to comparisons of human performance and chance mechanisms. A proposed developmental hierarchy suggests that all four categories embody basic cognitive structures that assist in detecting, decoding, and interpreting both inanimate and social aspects of the environment.

Assessing Gambler’s Fallacy in Children Through Framing and Executive Functioning

“…We made two predictions at the outset of our experiment: 1) that GF-like responding would show a positive correlation with EF; and 2) that as EF increases, children would show framing effects that begin to resemble those seen in adults. In adults, GF-like responding is more likely when assessing outputs of natural systems, while HHF-like responding is more likely when assessing outputs related to human agents (Ayton & Fischer, 2004;Burns & Corpus, 2004;Fischer & Savranevski, 2015). Therefore, we predicted that recency biases would show sensitivity to framing effects in our 7 to 8-year-old subjects -children who on average score higher on EF -but not our 4 to 5-year-old subjects.…”

“…How can we explain this discrepancy? We favor an explanation in which world-knowledge domains interact with increasing EF (Fischer & Savranevski, 2015;Simms et al, 2018;Bobrowicza et al, 2022).…”

“…spinning a roulette wheel) tends to bias subjects towards showing the GF bias. The same sequence framed as the product of human agency (e.g., shooting basketballs), instead biases subjects towards showing the HHF bias (Burns & Corpus, 2004;Ayton & Fischer, 2004;Fischer & Savranevski, 2015).…”

Predicting Outcomes in a Sequence of Binary Events: Belief Updating and Gambler's Fallacy Reasoning

“…When asked to predict future outcomes for sequences produced by intentional actors, people exhibit a hot hand pattern of increasing expectations that streaks of identical outcomes will repeat (Alter & Oppenheimer, 2006 ; Bar‐Eli, Avugos, & Raab, 2006 ; cf. Boynton, 2003 ; Gilovich, Vallone, & Tversky, 1985 ; Fischer & Savranevski, 2015 ; Vergin, 2001 ). Some researchers suggest observers believe there is something special about human performance (Ayton & Fischer, 2004 ), or about the intentional mind of human actors (Caruso, Waytz, & Epley, 2010 ; Roney & Trick, 2009 ).…”

Predicting Outcomes in a Sequence of Binary Events: Belief Updating and Gambler’s Fallacy Reasoning

“…When asked to predict future outcomes for sequences produced by intentional actors, people exhibit a hot hand pattern of increasing expectations that streaks of identical outcomes will repeat (Alter & Oppenheimer, 2006;Bar-Eli, Avugos, & Raab, 2006;cf. Boynton, 2003;Gilovich, Vallone, & Tversky, 1985;Fischer & Savranevski, 2015;Vergin, 2000). Some researchers suggest people believe there is something "special" about human performance (Ayton & Fischer, 2004), or about the intentional mind of human actors (Caruso, Waytz, & Epley, 2010;Roney & Trick, 2009).…”