Visual fixations and the computation and comparison of value in simple choice

Journal name:
Nature Neuroscience
Volume:
13,
Pages:
1292–1298
Year published:
DOI:
doi:10.1038/nn.2635
Received
Accepted
Published online
Corrected online

Abstract

Most organisms facing a choice between multiple stimuli will look repeatedly at them, presumably implementing a comparison process between the items' values. Little is known about the nature of the comparison process in value-based decision-making or about the role of visual fixations in this process. We created a computational model of value-based binary choice in which fixations guide the comparison process and tested it on humans using eye-tracking. We found that the model can quantitatively explain complex relationships between fixation patterns and choices, as well as several fixation-driven decision biases.

At a glance

Figures

  1. Experiment and model.
    Figure 1: Experiment and model.

    (a) Choice trial. Subjects are forced to fixate at the center of the screen for 2 s. They are then presented with images of two items and given as much time as they want to make their choice. After a selection is made a yellow box highlights the chosen item for 1 s. RT, reaction time. (b) Model. A relative decision value (RDV) evolves over time with a slope that is biased toward the item that is being fixated. The slope dictates the average rate of change of the RDV, but there is also an error term drawn from a Gaussian distribution. When the RDV hits the barrier a choice is made for the corresponding item. The shaded vertical regions represent the item being fixated. (c,d) Simulated runs of the model using d = 0.005, σ = 0.05 and θ = 0.6, to give a better intuition for the decision process.

  2. Basic psychometrics.
    Figure 2: Basic psychometrics.

    (a) Psychometric choice curve. P, probability. (b) Reaction times as a function of the difference in liking ratings between the best and worst items, which is a measure of difficulty. (c) Number of fixations in a trial as a function of choice difficulty. The black dashed lines indicate the simulated data using the MLE parameters. Subject data includes only odd-numbered trials. In a, the gray dash-dotted line indicates the simulated data for the θ = 0 model. Bars denote s.e., clustered by subject. Tests are based on a paired two-sided t-test.

  3. Fixation properties.
    Figure 3: Fixation properties.

    (a) Probability that the first fixation is to the best item. In all cases they are not significantly different from 50%. (b) Middle fixation duration as a function of the liking rating of the fixated item. (c) Middle fixation duration as a function of the difference in liking ratings between the fixated and unfixated items. (d) Middle fixation duration as a function of the difference in liking ratings between the best- and worst-rated items. Bars denote s.e., clustered by subject. Tests are based on a paired two-sided t-test.

  4. Basic model predictions.
    Figure 4: Basic model predictions.

    (a) Fixation duration by type. Middle fixations indicate any fixations that were not the first or last fixations of the trial. (b) Probability that the last fixation is to the chosen item as a function of the difference in liking ratings between the fixated and unfixated items in that last fixation. (c) Amount of time spent looking more at Item B before the last fixation (to Item A), as a function of the duration of that last fixation. The black dashed line indicates the simulated data using the MLE parameters. Subject data includes only odd-numbered trials. In b, the gray dash-dotted line indicates the simulated data for the θ = 0 model, and the vertical dotted lines indicate the points at which the simulation curves cross the horizontal line at chance. In c, the gray dash-dotted line indicates the simulated data for the θ = 1 model. Bars denote s.e., clustered by subject.

  5. Choice biases.
    Figure 5: Choice biases.

    (a) Psychometric choice curve conditional on the location of the last fixation. (b) Probability that left is chosen as a function of the excess amount of time for which the left item was fixated during the trial. (c) Analogous to b, except subtracting the probability of choosing left for each difference in liking ratings. (d) Probability that the first-seen item is chosen as a function of the duration of that first fixation. (e) Analogous to d, except subtracting the probability of choosing the first-seen item for each difference in liking ratings. (f) Probability of choosing left as a function of the probability of looking left first. Each circle represents a different subject. The black dashed line indicates the simulated data using the MLE parameters. The gray dash-dotted line indicates the simulated data for the θ = 1 model. Subject data includes only odd-numbered trials. Bars denote s.e., clustered by subject. Tests are based on a paired two-sided t-test, except in f, where we used standard two-sided t-tests.

  6. Alternative models.
    Figure 6: Alternative models.

    (a,b) Replications of Figures 5b and 2c for alternative model 1. (c,d) Replications of Figures 5a and 4c for alternative model 2. (e) Replication of Figure 5b for alternative model 3. The black dashed lines indicate the simulated data using the alternative models. Subject data includes only odd-numbered trials. Bars denote s.e., clustered by subject. Tests are based on paired two-sided t-tests.

Change history

Corrected online 10 February 2011
In the version of this article initially published, there were symbols dropped from the equations in the second paragraph of the results section. The term θright should have been θrright in the first equation and the term θleft should have been θrleft in the second equation. The error has been corrected in the HTML and PDF versions of the article.

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Author information

Affiliations

  1. Division of Humanities and Social Sciences, California Institute of Technology, Pasadena, California, USA.

    • Ian Krajbich &
    • Antonio Rangel
  2. Precourt Institute for Energy Efficiency, Stanford University, Palo Alto, California, USA.

    • Carrie Armel
  3. Computational and Neural Systems, California Institute of Technology, Pasadena, California, USA.

    • Antonio Rangel

Contributions

A.R. and C.A. devised the experiment. I.K. programmed and conducted the experiment, performed the analyses and co-wrote the manuscript. A.R. designed the model, co-wrote the manuscript and supervised the project.

Competing financial interests

The authors declare no competing financial interests.

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    Supplementary Figures 1–30 and Supplementary Table 1

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