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Mapping internal states to formal systems: modeling human numerosity estimation

Whether estimating the size of a crowd, thinking about how heavy something will be before trying to lift it, or reviewing a restaurant on a five-star scale, the modern world frequently requires us to navigate between subjective sensory experiences and shared formal systems. This entails mapping internal variables onto a common scale. Here we ask how people manage this in the case of estimating number. We present people with arrays of dots and ask them to report how many dots there are. In Experiment 1, we test predictions made by existing models of how people map from internal representations of numerosity to verbal estimates. We find that people’s estimates do not have a stable coefficient of variation at higher magnitudes, as has previously been suggested, and that the likely cause of this is a “drift” in people’s estimate calibration over many trials. Building on these results, we present a model of the mapping function from subjective numerosity to formal number estimates which relies only on a limited set of previous estimates and a rough sensitivity to the distribution of numbers in the world. Our model is able to generate an accurate mapping with limited data, as well as reproduce the notable aspects of human estimation described in our experimental results, namely humanlike patterns of underestimation, individual variability, and dynamic miscalibration at higher magnitudes.