Sources of error in numerical estimation: Insights from the wisdom of crowds effect

Could the average estimate of a class of kindergartners be more accurate than any adult estimate? Normally, yes: a "wisdom of crowds" (WoC) effect would be observed if individual estimates were independent and unbiased, leading any crowd of children to outperform any individual adult. However, children's estimates have been proposed to be biased by logarithmic encoding of numerical value, which would undermine the WoC effect. Here, we examined the WoC effect to test whether estimates reflect bias (e.g., logarithmic encoding), noise (e.g., uncertainty), or both. In Study 1, 80 4- to 7-year-olds and 80 adults were asked to estimate the number of dots on a number line, and we found that WoC effects and effects of crowd size were stronger on 0-30 than 0-100 number-lines. In Study 2, 80 children and 80 adults completed a symbolic number-line task, and we found similar effects. In both studies, we also compared a crowd of less-advanced with individual more-advanced children. Again, the WoC effect was stronger on 0-30 than 0-100 number lines. Overall, results provide further evidence that development of numerical estimation involves reducing bias (especially for large numbers), not just reducing noise. Implications for theories of number representation are discussed.