Constrained representations of numerical magnitudes
Arthur Prat-Carrabin, Michael Woodford, Columbia University, United States
Posters 2 Poster
Pacific Ballroom H-O
Fri, 26 Aug, 19:30 - 21:30 Pacific Time (UTC -8)
Humans are imprecise in their representations of magnitudes, resulting in suboptimal estimations and decisions. This imprecision is thought to result from cognitive constraints, but the nature of these constraints remains unclear. If representations are efficient, however, they should be adapted to the prior distribution of the magnitudes, in a way that depends on the constraints. In two tasks involving numbers presented as clouds of dots or as Arabic numerals, we sample these numbers from a uniform distribution, whose width we manipulate across blocks of trials. We find that the variance of subjects' numerical estimates is a linear function of the width of the prior, rather than the square of this width. Subjects are thus relatively more precise with wider priors. Their behaviors in the two tasks are best captured by the same model, in which the same formula specifies the brain's resource constraint. Our results, consistent across two task modalities, exhibit how subjects' precision varies with the prior, and shed light on the cognitive constraints weighing on the brain's representations.