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Using Occam's razor and Bayesian modelling to compare discrete and continuous representations in numerosity judgements.

Spicer, Jake and Sanborn, Adam N. and Beierholm, Ulrik R. (2020) 'Using Occam's razor and Bayesian modelling to compare discrete and continuous representations in numerosity judgements.', Cognitive psychology., 122 . p. 101309.


Previous research has established that numeric estimates are based not just on perceptual data but also past experience, and so may be influenced by the form of this stored information. It remains unclear, however, how such experience is represented: numerical data can be processed by either a continuous analogue number system or a discrete symbolic number system, with each predicting different generalisation effects. The present paper therefore contrasts discrete and continuous prior formats within the domain of numerical estimation using both direct comparisons of computational models of this process using these representations, as well as empirical contrasts exploiting different predicted reactions of these formats to uncertainty via Occam’s razor. Both computational and empirical results indicate that numeric estimates commonly rely on a continuous prior format, mirroring the analogue approximate number system, or ‘number sense’. This implies a general preference for the use of continuous numerical representations even where both stimuli and responses are discrete, with learners seemingly relying on innate number systems rather than the symbolic forms acquired in later life. There is however remaining uncertainty in these results regarding individual differences in the use of these systems, which we address in recommendations for future work.

Item Type:Article
Full text:Publisher-imposed embargo until 03 July 2021.
(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
File format - PDF
Publisher Web site:
Publisher statement:© 2020 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Date accepted:23 May 2020
Date deposited:28 May 2020
Date of first online publication:2020
Date first made open access:03 July 2021

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