Selective overweighting of larger magnitudes during noisy numerical comparison

Abstract

Humans are often required to compare average magnitudes in numerical data; for example, when comparing product prices on two rival consumer websites. However, the neural and computational mechanisms by which numbers are weighted, integrated and compared during categorical decisions are largely unknown1,2,3,4,5. Here, we show a systematic deviation from ‘optimality’ in both visual and auditory tasks requiring averaging of symbolic numbers. Participants comparing numbers drawn from two categories selectively overweighted larger numbers when making a decision, and larger numbers evoked disproportionately stronger decision-related neural signals over the parietal cortex. A representational similarity analysis6 showed that neural (dis)similarity in patterns of electroencephalogram activity reflected numerical distance, but that encoding of number in neural data was systematically distorted in a way predicted by the behavioural weighting profiles, with greater neural distance between adjacent larger numbers. Finally, using a simple computational model, we show that although it is suboptimal for a lossless observer, this selective overweighting policy paradoxically maximizes expected accuracy by making decisions more robust to noise arising during approximate numerical integration2. In other words, although selective overweighting discards decision information, it can be beneficial for limited-capacity agents engaging in rapid numerical averaging.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Task, model simulations and human behaviour.
Figure 2: Overview of model results and simulations for each experiment and condition.
Figure 3: CPP analysis.
Figure 4: Representational similarity analysis.

References

  1. 1

    Tsetsos, K., Chater, N. & Usher, M. Salience driven value integration explains decision biases and preference reversal. Proc. Natl Acad. Sci. USA 109, 9659–9664 (2012).

    CAS  Article  Google Scholar 

  2. 2

    Tsetsos, K. et al. Economic irrationality is optimal during noisy decision making. Proc. Natl Acad. Sci. USA 113, 3102–3107 (2016).

    CAS  Article  Google Scholar 

  3. 3

    Brezis, N., Bronfman, Z. Z., Jacoby, N., Lavidor, M. & Usher, M. Transcranial direct current stimulation over the parietal cortex improves approximate numerical averaging. J. Cogn. Neurosci. 28, 1700–1713 (2016).

    Article  Google Scholar 

  4. 4

    Brezis, N., Bronfman, Z. Z. & Usher, M. Adaptive spontaneous transitions between two mechanisms of numerical averaging. Sci. Rep. 5, 10415 (2015).

    CAS  Article  Google Scholar 

  5. 5

    Malmi, R. A. & Samson, D. J. Intuitive averaging of categorized numerical stimuli. J. Verbal Learning Verbal Behav. 22, 547–559 (1983).

    Article  Google Scholar 

  6. 6

    Kriegeskorte, N. & Kievit, R. A. Representational geometry: integrating cognition, computation, and the brain. Trends Cogn. Sci. 17, 401–412 (2013).

    Article  Google Scholar 

  7. 7

    Scott, B. B., Constantinople, C. M., Erlich, J. C., Tank, D. W. & Brody, C. D. Sources of noise during accumulation of evidence in unrestrained and voluntarily head-restrained rats. eLife 4, e11308 (2015).

    Article  Google Scholar 

  8. 8

    Wyart, V. & Koechlin, E. Choice variability and suboptimality in uncertain environments. Curr. Opin. Behav. Sci. 11, 109–115 (2016).

    Article  Google Scholar 

  9. 9

    Gibbon, J. Scalar expectancy theory and Weber’s law in animal timing. Psychol. Rev. 84, 279–325 (1977).

    Article  Google Scholar 

  10. 10

    Moyer, R. S. & Landauer, T. K. Time required for judgements of numerical inequality. Nature 215, 1519–1520 (1967).

    CAS  Article  Google Scholar 

  11. 11

    Dehaene, S., Dupoux, E. & Mehler, J. Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison. J. Exp. Psychol. Hum. Percept. Perform. 16, 626–641 (1990).

    CAS  Article  Google Scholar 

  12. 12

    Van Opstal, F., de Lange, F. P. & Dehaene, S. Rapid parallel semantic processing of numbers without awareness. Cognition 120, 136–147 (2011).

    Article  Google Scholar 

  13. 13

    Kelly, S. P. & O’Connell, R. G. Internal and external influences on the rate of sensory evidence accumulation in the human brain. J. Neurosci. 33, 19434–19441 (2013).

    CAS  Article  Google Scholar 

  14. 14

    O’Connell, R. G., Dockree, P. M. & Kelly, S. P. A supramodal accumulation-to-bound signal that determines perceptual decisions in humans. Nat. Neurosci. 15, 1729–1735 (2012).

    Article  Google Scholar 

  15. 15

    Nili, H. et al. A toolbox for representational similarity analysis. PLoS Comput. Biol. 10, e1003553 (2014).

    Article  Google Scholar 

  16. 16

    Woodford, M. Prospect theory as efficient perceptual distortion. Am. Econ. Rev. 102, 41–46 (2012).

    Article  Google Scholar 

  17. 17

    Li, V. L., Castañón, S. H., Solomon, J. A., Vandormael, H. & Summerfield, C. Robust averaging protects decisions from noise in neural computations. Preprint at bioRxiv https://doi.org/10.1101/147744 (2017).

  18. 18

    Twomey, D. M., Murphy, P. R., Kelly, S. P. & O’Connell, R. G. The classic P300 encodes a build-to-threshold decision variable. Eur. J. Neurosci. 42, 1636–1643 (2015).

    Article  Google Scholar 

  19. 19

    Donchin, E. & Coles, M. G. H. Is the P300 component a manifestation of context updating? Behav. Brain Sci. 11, 357–374 (1988).

    Article  Google Scholar 

  20. 20

    Sutton, S., Braren, M., Zubin, J. & John, E. R. Evoked-potential correlates of stimulus uncertainty. Science 150, 1187–1188 (1965).

    CAS  Article  Google Scholar 

  21. 21

    Picton, T. W. The P300 wave of the human event-related potential. J. Clin. Neurophysiol. 9, 456–479 (1992).

    CAS  Article  Google Scholar 

  22. 22

    Bulthé, J., De Smedt, B. & Op de Beeck, H. P. Visual number beats abstract numerical magnitude: format-dependent representation of Arabic digits and dot patterns in human parietal cortex. J. Cogn. Neurosci. 27, 1376–1387 (2015).

    Article  Google Scholar 

  23. 23

    Eger, E. et al. Deciphering cortical number coding from human brain activity patterns. Curr. Biol. 19, 1608–1615 (2009).

    CAS  Article  Google Scholar 

  24. 24

    Harvey, B. M., Klein, B. P., Petridou, N. & Dumoulin, S. O. Topographic representation of numerosity in the human parietal cortex. Science 341, 1123–1126 (2013).

    CAS  Article  Google Scholar 

  25. 25

    Dehaene, S. The organization of brain activations in number comparison: event-related potentials and the additive-factors method. J. Cogn. Neurosci. 8, 47–68 (1996).

    CAS  Article  Google Scholar 

  26. 26

    Libertus, M. E., Woldorff, M. G. & Brannon, E. M. Electrophysiological evidence for notation independence in numerical processing. Behav. Brain Funct. 3, 1 (2007).

    Article  Google Scholar 

  27. 27

    Wyart, V., Myers, N. E. & Summerfield, C. Neural mechanisms of human perceptual choice under focused and divided attention. J. Neurosci. 35, 3485–3498 (2015).

    CAS  Article  Google Scholar 

  28. 28

    Ille, N., Berg, P. & Scherg, M. Artifact correction of the ongoing EEG using spatial filters based on artifact and brain signal topographies. J. Clin. Neurophysiol. 19, 113–124 (2002).

    Article  Google Scholar 

  29. 29

    Spitzer, B., Blankenburg, F. & Summerfield, C. Rhythmic gain control during supramodal integration of approximate number. NeuroImage 129, 470–479 (2016).

    Article  Google Scholar 

  30. 30

    Grootswagers, T., Wardle, S. G. & Carlson, T. A. Decoding dynamic brain patterns from evoked responses: a tutorial on multivariate pattern analysis applied to time series neuroimaging data. J. Cogn. Neurosci. 29, 677–697 (2017).

    Article  Google Scholar 

  31. 31

    Nili, H., Walther, A., Alink, A. & Kriegeskorte, N. Inferring exemplar discriminability in brain representations. Preprint at bioRxiv https://doi.org/10.1101/080580 (2016).

  32. 32

    Maris, E. & Oostenveld, R. Nonparametric statistical testing of EEG- and MEG-data. J. Neurosci. Methods 164, 177–190 (2007).

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by grants from the German Research Foundation to B.S. (DFG SP 1510/1-1 and DFG SP 1510/2-1) and a European Research Council Starter Grant (281628) to C.S. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript. We thank V. Li, T. Flesch and H. Nili for helpful suggestions and scripts, F. Blankenburg for resources, A. Epure for help with data acquisition and R. Kievit for helpful comments on a previous version of the manuscript.

Author information

Affiliations

Authors

Contributions

B.S. designed the experiments with contributions from L.W. and C.S. L.W. and B.S. conducted the experiments. B.S. and C.S. developed the analysis approach. B.S. analysed the data with contributions from C.S. B.S. and C.S. wrote the paper.

Corresponding author

Correspondence to Bernhard Spitzer.

Ethics declarations

Competing interests

The authors declare no competing interests.

Supplementary information

Supplementary Information

Supplementary Methods, Supplementary Figures 1–3

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Spitzer, B., Waschke, L. & Summerfield, C. Selective overweighting of larger magnitudes during noisy numerical comparison. Nat Hum Behav 1, 0145 (2017). https://doi.org/10.1038/s41562-017-0145

Download citation

Further reading