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Reply to: Divisive normalization does influence decisions with multiple alternatives

Nature Human Behaviour volume 4, pages 1121–1123 (2020)Cite this article

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The Original Article was published on 14 September 2020

replying to R. Webb et al. Nature Human Behaviour https://doi.org/s41562-020-00941-5 (2020)

The divisive normalization (DN) model assumes that a canonical neural computation exerts a measurable influence on value-based decisions between three or more alternatives. More specifically, it predicts that the relative preference for the best option compared with the second-best option decreases as the sum of all subjective values increases. This constitutes a violation of the axiom of independence of irrelevant alternatives (IIA). Although the study by Louie et al.1 seemed to provide support for the DN model, our high-powered direct replication of this study together with a separate eye-tracking experiment showed that the proposed violations were neither replicable nor robust2. Webb et al.3 have now reanalysed our direct replication data and claim to find evidence in favour of a more recent version of the DN model when comparing it with standard economic models that are tied to the IIA axiom. Here, we reproduce and extend these analyses. We can confirm the improvement of the model fit of the new DN model. More importantly, however, we show that the fit can be further improved in many more participants by allowing the model to make predictions that go against the rationale of DN. Our results raise general doubts about how behavioural implications of neural computations can be tested convincingly and underscore the need for process models of decision-making.

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Fig. 1: Parameter estimates, model fit and predictions.

Data availability

The data analysed for this work are publicly available on the Open Science Framework (https://osf.io/qrv2e/).

Code availability

The custom code for the analyses reported here is publicly available on the Open Science Framework (https://osf.io/qrv2e/).

References

  1. Louie, K., Khaw, M. W. & Glimcher, P. W. Normalization is a general neural mechanism for context-dependent decision making. Proc. Natl Acad. Sci. USA 110, 6139–6144 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  2. Gluth, S., Kern, N., Kortmann, M. & Vitali, C. L. Value-based attention but not divisive normalization influences decisions with multiple alternatives. Nat. Hum. Behav. 4, 634–645 (2020).

    Article  PubMed  PubMed Central  Google Scholar 

  3. Webb, R., Glimcher, P. W. & Louie, K. Divisive normalization does influence decisions with multiple alternatives. Nat. Hum. Behav. https://doi.org/s41562-020-00941-5 (2020).

  4. Webb, R., Glimcher, P. W. & Louie, K. The normalization of consumer valuations: context-dependent preferences from neurobiological constraints. Manag. Sci. https://doi.org/10.1287/mnsc.2019.3536 (2020).

  5. Lee, M. D. & Wagenmakers, E.-J. Bayesian Cognitive Modeling: A Practical Course (Cambridge Univ. Press, 2013).

  6. Farrell, S. & Lewandowsky, S. Computational Modeling of Cognition and Behavior (Cambridge Univ. Press, 2018).

  7. Carandini, M. & Heeger, D. J. Normalization as a canonical neural computation. Nat. Rev. Neurosci. 13, 51–62 (2012).

    Article  CAS  Google Scholar 

  8. De Martino, B., Fleming, S. M., Garrett, N. & Dolan, R. J. Confidence in value-based choice. Nat. Neurosci. 16, 105–110 (2013).

    Article  PubMed  Google Scholar 

  9. Lebreton, M., Abitbol, R., Daunizeau, J. & Pessiglione, M. Automatic integration of confidence in the brain valuation signal. Nat. Neurosci. 18, 1159–1167 (2015).

    Article  CAS  PubMed  Google Scholar 

  10. Busemeyer, J. R., Gluth, S., Rieskamp, J. & Turner, B. M. Cognitive and neural bases of multi-attribute, multi-alternative, value-based decisions. Trends Cogn. Sci. 23, 251–263 (2019).

    Article  PubMed  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Psychology, University of Basel, Basel, Switzerland

    Sebastian Gluth, Nadja Kern & Cécile L. Vitali

Authors
  1. Sebastian Gluth
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  2. Nadja Kern
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  3. Cécile L. Vitali
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Contributions

S.G. analysed the data and wrote the manuscript. N.K. and C.L.V. revised the manuscript.

Corresponding author

Correspondence to Sebastian Gluth.

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The authors declare no competing interests.

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Extended data

Extended Data Fig. 1 Parameter estimates based on hierarchical Bayesian modeling.

Parameter estimates for ω (based on hierarchical Bayesian modeling) when this parameter is forced to be ≥0 (as assumed by DN; blue) or not (red). Note the shrinkage of individual estimates as compared to the estimates based on maximum likelihood presented in Fig. 1a.

Extended Data Fig. 2 Modeling results of the eye-tracking experiment dataset.

Note that the very large 95% CI for participants with ω > 0 in c is due to the fact that there were only very few participants with a positive estimate of this parameter.

Extended Data Fig. 3 Model comparison of the eye-tracking experiment dataset.

Definitions of the abbreviations are provided in Table 1.

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Supplementary methods and references.

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Gluth, S., Kern, N. & Vitali, C.L. Reply to: Divisive normalization does influence decisions with multiple alternatives. Nat Hum Behav 4, 1121–1123 (2020). https://doi.org/10.1038/s41562-020-00942-4

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