Intrinsic whole number bias in humans.

Abstract

Humans have great difficulty comparing quotients including fractions, proportions, and probabilities and often erroneously isolate the whole numbers of the numerators and denominators to compare them. Some have argued that the whole number bias is a compensatory strategy to deal with difficult comparisons. We examined adult humans' preferences for gambles that differed only in numerosity, and not in factors that influence their expected value (probabilities and stakes). Subjects consistently preferred gambles with more winning balls to ones with fewer, even though the probabilities were mathematically identical, replicating prior results. In a second experiment, we found that subjects accurately represented the relative probabilities of the choice options during rapid nonverbal probability judgments but nonetheless showed biases based on whole numbers. We mathematically formalized and quantitatively evaluated cognitive rules based on existing hypotheses that attempt to explain subjects' whole number biases during quotient comparisons. The results show that the whole number bias is intrinsic to the way humans solve quotient comparisons rather than a compensatory strategy. (PsycINFO Database Record

The numerator bias exists in millions of real-world comparisons

“…As expected, we found that the bias changes with the probability of observing a large numerator in the larger fraction. Perhaps more interesting, we replicated previous findings that the bias persists in the balanced 50/50 condition (Alonso-Diaz et al, 2018;Fabbri, Caviola, Tang, Zorzi, & Butterworth, 2012). It is a common but strange result for the adaptation theory: with balanced probabilities, the bias should disappear, i.e., picking based on the numerator will lead to chance-behavior.…”

“…For instance, in fractals, there is self-similarity regardless of scale. If the independence of object size and ratios marks our visual experience, then the whole-number bias may be grounded on perceptions, making it universal and perseverant (Alonso-Diaz, Cantlon, & Piantadosi, 2019).…”

“…Therefore, the strategy is not necessarily a capacity issue (Alonso-Diaz, Piantadosi, Hayden, & Cantlon, 2018).…”

“…The numerator bias is a cognitive illusion occurring in education, decision-making, and perception (Ni & Zhou, 2005;Reyna & Brainerd, 2008). There are a handful of explanations, ranging from quality of education (Siegler, Fazio, Bailey, & Zhou, 2013), strategic behavior (Fazio, DeWolf, & Siegler, 2016), the undue weighting of raw numerical information (Alonso-Diaz et al, 2018), and use of dual-systems, such as an intuitive rather than a rational system (Denes-Raj & Epstein, 1994).…”

Math matters: A novel, brief educational intervention decreases whole number bias when reasoning about COVID-19.

“…For example, for the ratio 15/30, people may think about the numerator, 15, or the denominator, 30, as whole numbers in isolation rather than as parts of a ratio (15/30 = ½ = 50% = 0.50). People of different ages (Alibali & Sidney, 2015; Braithwaite & Siegler, 2018; Fazio et al, 2016; Fitzsimmons et al, 2020; Ni & Zhou, 2005; Opfer & Devries, 2008), expertise levels (Obersteiner et al, 2013), and cultures (Alonso-Diaz et al, 2019; DeWolf & Vosniadou, 2015; Gómez et al, 2015; Van Hoof et al, 2020) make WNB errors. Reasoning about the magnitude of ratios compared to whole numbers is more effortful, error-prone, and time-consuming (e.g., Fazio et al, 2014; Siegler et al, 2011; Yu et al, 2020).…”