Ongoing Dynamic Calibration Produces Unstable Number Estimates

Whether estimating the size of a crowd or rating a restaurant on a five-star scale, humans frequently navigate between subjective sensory experiences and shared formal systems. Here we ask how people manage this in the case of estimating number. We present participants with arrays of dots and ask them to report how many dots there are. Our results produce two novel findings. First, people's estimates are best fit by a bilinear function in log space, rather than the traditional power law described in previous literature. Second, we find that people's estimates do not have a stable coefficient of variation at higher magnitudes, and that the likely cause of this is a "drift" in people's estimate calibration over many trials which has not previously been identified. Building on these results, we present a model of the mapping function from subjective numerosity to symbolic number that relies primarily on a constrained set of previous estimates and familiar numerosities, rather than the robust internal scale used in existing models. Our model is able to generate an accurate mapping with limited data and reproduce notable aspects of estimation seen in our experimental results. This suggests that human number estimation, and perhaps other domains in which we must navigate between subjective representations and formal systems, is governed by a relatively simple decision process that primarily seeks to maintain consistency with previous estimates.