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A unified account of numerosity perception

Nature Human Behaviour volume 4, pages 1265–1272 (2020)Cite this article

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Abstract

People can identify the number of objects in sets of four or fewer items with near-perfect accuracy but exhibit linearly increasing error for larger sets. Some researchers have taken this discontinuity as evidence of two distinct representational systems. Here, we present a mathematical derivation showing that this behaviour is an optimal representation of cardinalities under a limited informational capacity, indicating that this behaviour can emerge from a single system. Our derivation predicts how the amount of information accessible to viewers should influence the perception of quantity for both large and small sets. In a series of four preregistered experiments (N = 100 each), we varied the amount of information accessible to participants in number estimation. We find tight alignment between the model and human performance for both small and large quantities, implicating efficient representation as the common origin behind key phenomena of human and animal numerical cognition.

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Fig. 1: Response distributions for two possible forms of Q, with probabilities of estimates for numerosities 1–6.
Fig. 2: The model’s posterior probability over numerosities, when shown 1 to 15 objects.
Fig. 3: Model posterior predictive fits including participant effects and human data for absolute estimation error, mean estimates and the shape of the response distributions.
Fig. 4: Mean estimates and absolute error of the estimates as a function of number shown in the three replication experiments.

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Data availability

The anonymized data from the experiments have been posted at the Open Science Foundation at https://osf.io/svcy5/.

Code availability

The code for the model can be found at https://github.com/samcheyette/info_theory_number.

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Acknowledgements

We thank F. Callaway, J. Cantlon and E. Gibson for providing feedback on an earlier draft of this paper. This work was supported by grants no. 1760874 and no. 2000759 from the National Science Foundation, Division of Research on Learning (to S.T.P.) and award no. 1R01HD085996 from the Eunice Kennedy Shriver National Institute of Child Health & Human Development (NICHD) at the National Institutes of Health (to S.T.P. and J. Cantlon). The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

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Authors and Affiliations

  1. Department of Psychology, UC Berkeley, Berkeley, CA, USA

    Samuel J. Cheyette & Steven T. Piantadosi

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  1. Samuel J. Cheyette
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  2. Steven T. Piantadosi
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Contributions

S.J.C. and S.T.P. derived and implemented the model. S.J.C. and S.T.P. designed the experiment. S.J.C. implemented the experiment and analysed the data. S.J.C. and S.T.P. wrote the paper.

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Correspondence to Samuel J. Cheyette.

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The authors declare no competing interests.

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Supplementary Figs. 1 and 2, Supplementary Table 1, Supplementary Results and Supplementary References.

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Cheyette, S.J., Piantadosi, S.T. A unified account of numerosity perception. Nat Hum Behav 4, 1265–1272 (2020). https://doi.org/10.1038/s41562-020-00946-0

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