Wagers for work: Decomposing the costs of cognitive effort

Abstract

Some aspects of cognition are more taxing than others. Accordingly, many people will avoid cognitively demanding tasks in favor of simpler alternatives. Which components of these tasks are costly, and how much, remains unknown. Here, we use a novel task design in which subjects request wages for completing cognitive tasks and a computational modeling procedure that decomposes their wages into the costs driving them. Using working memory as a test case, our approach revealed that gating new information into memory and protecting against interference are costly. Critically, other factors, like memory load, appeared less costly. Other key factors which may drive effort costs, such as error avoidance, had minimal influence on wage requests. Our approach is sensitive to individual differences, and could be used in psychiatric populations to understand the true underlying nature of apparent cognitive deficits.

Fig 1. The behavioral paradigm & computational modeling approach.

Before each round of the experiment, subjects were shown an image which was associated with one of three possible tasks. They then indicated the wages (in points) that they would like to receive for completing 1 round of that task. If their fair wage rating was below a random computer offer, then they would complete that task and receive the computer’s offer. If their fair wage was above a random computer offer, then they would complete a different, easier task instead. We employed this inversion of the Becker-Degroot-Marschak auction procedure to incentivize subjects to be truthful in their fair wage ratings. The fractal images in this figure were obtained under a Creative Commons Zero 1.0 Public Domain License (https://creativecommons.org/publicdomain/zero/1.0/) from openclipart.org (https://openclipart.org/detail/300064/colorful-abstract-background and https://openclipart.org/detail/310263/another-abstract-background).

Fig 2. Model-agnostic behavioral results.

A. Distributions of mean accuracies across all subjects for the default task (1-detect), and the three rated tasks (1-back, 3-detect, and 2-back). The black bars depict the means and standard errors of the mean (SEMs) of each distribution. The distribution of all subjects’ mean accuracies was plotted using a Gaussian kernel via violin.m. All mean accuracies for each task were significantly different from each other (all p’s < 0.001). B. Distributions of mean fair wages across all subjects for the three rated tasks. The lowest possible rating was 1, and the highest possible rating was 5. The black bars depict the means and SEMs of each distribution. The distribution of ratings was plotted using violin.m. **** indicates significance at the p < 0.0001 level. C. Mean accuracy across all subjects on each iteration of each task. Due to the stochasticity inherent to the BDM auction procedure, individual subjects completed the 1-back, 3-detect, and 2-back tasks a variable number of times, but a maximum of 11 times each. The relative number of subjects who completed each iteration is depicted by the size of the dot plotted at the mean. Error bars are SEMs. A two-way ANOVA of task and task iteration revealed a main effect of task identity (F = 15, p < 0.0001) but no effect of task iteration (F = 1.3, p > 0.05). Thus mean accuracy was different across tasks but did not change with task experience. D. Mean fair wage rating by rating number, where the maximum is 11 ratings of one task. A 2-way ANOVA on BDM ratings showed a main effect of task identity (Table 1; F = 33; p < 0.0001) and a main effect of task iteration (Fig 1; F = 21; p < 0.0001). Error bars are SEMs.

Fig 3. Computational modeling results.

A. The number of subjects best fit by each model with a non-zero model frequency. Of the 84 computational models fit to subjects’ fair wages, the winning models were alpha cost-learning models containing update costs (c_update), interference costs (c_interference), and maintenance costs (c_maintenance), and false alarm costs (c_fa), in various combinations. The model with the highest model frequency was the model including update costs alone. B. The mean of the posterior distribution of each cost parameter from the models that best fit at least 1 subject’s fair wages. These posterior distributions were calculated by combining inferred parameter distributions across subjects and across models. Inference was performed over joint 4D distributions to capture co-variance between update, interference, maintenance, and false alarm costs. For plotting purposes we summed over the three irrelevant dimensions for each parameter to construct its marginal distribution, and then calculated the means and variances of the marginals. Error bars reflect the hierarchical standard error of the mean; they were calculated not with the square root of the total number of subjects in the denominator, but with the square root of the number of subjects’ data explained by models containing that parameter. Note that the error bars describe the spread of the marginal parameter distributions, not variance in the fitting process, and thus are not suitable for estimating the statistical significance of the effects plotted. C. Real (solid lines) versus simulated (dashed lines) fair wage ratings on each rating iteration for each task. Data simulated using each subjects’ best model faithfully reproduces real subject data (r² = 0.52).

Fig 4. Winning model parameter values by Need for Cognition (NFC) Group.

Mean parameter magnitudes from the winning 6-parameter update cost model. σ is the standard deviation parameter which dictates how noisy each subject’s fair wage ratings are, on average. α is the subject-specific task cost-learning rate. The update cost is the magnitude of the influence of WM updates on each subject’s fair wage ratings. The init parameters dictate each subject’s initial fair wage for each task. Subjects were split into NFC tertiles resulting in low (N = 25), mid (N = 37), and high (N = 37) NFC groups. Fit parameter values were then averaged within-group to produce each bar. Error bars are standard error of the mean. * indicates significant difference as assessed with a t-test at p < 0.05 level. ** p < 0.01.