Proceedings of the Annual Meeting of the Cognitive Science Society

There are ongoing debates whether logarithmic compression in number-to-space mapping reflects logarithmic encoding of large numbers (bias) or uncertainty about numeric value (noise). We tested these two hypotheses by disentangling the effect of bias and noise. When 80 adults and 80 4- to 7-year-olds were asked to estimate the number of dots on a number line, both children and adults were more logarithmic on 0-100 than 0-30 problems. Internal noise explained some of the variance in logarithmicity, but only for children. We then examined the wisdom of crowds effect by comparing accuracy of children's mean estimate with accuracy of each adult's estimates. As predicted, children as a crowd were not as accurate as individual adults, indicating that noise is not the only source of children's errors. Generally, increasing the size of a crowd also had a smaller effect on 0-100 than 0-30 problems, indicating that inaccuracy on 0-30 problems is likely due to noise. The present study provides evidence that bias and noise have an additive effect on logarithmic compression and that children's logarithmicity reflects bias in number representations, not just noise.