Fig 1.
Information seeking task design.
(A) Subjects aim to select the “winning row” (in this example, the row with the largest product). After the first card is revealed (here, the 7 of diamonds), subjects enter Task Stage 1. Here, they choose between the two yellow options, either sampling another card (costing 10 points) or making a guess about which is the winning row (no cost). Greyed-out cards cannot yet be sampled. If choosing to sample, then Task Stage 2 is entered, in which either remaining card may be sampled (costing 15 points) or the subject may again guess. In Task Stage 3, sampling the last remaining card costs 20 points. At any Task Stage, making a guess means that subjects enter the Choice Stage. Here, after choosing, all cards are revealed and the subjected either wins 60 points if correct, or loses 50 points if incorrect. (B) The six task conditions in a 3-by-2 design. Subjects either select the row with biggest (or smallest) sum, the biggest (or smallest) product, or the biggest (or smallest) single card.
Fig 2.
Positive evidence approach bias at Task Stage 1.
At Task Stage 1, subjects decide whether to make a guess or pay 10 points to sample. The available card to sample may be on the same row (“AA trials”) or the opposite row (“AB trials”) as the first card. (A) Model predictions. The relative expected value (in points) of guessing versus sampling from the dynamic programming model in the MULTIPLY conditions. Mid-valued cards make it more valuable to sample, whereas extreme-valued cards make it more valuable to guess. There is a weaker influence of the location of available information (compare “AA trials” versus “AB trials”). Crucially, optimal behavior is identical for both MULTIPLY BIG and MULTIPLY SMALL conditions. (B) Subject behavior. The probability of guessing in both conditions shows a broad similarity to the predictions of the dynamic programming model, but behavior in MULTIPLY BIG and MULTIPLY SMALL shows systematic differences. (See S1 Fig for AA and AB trials plotted together, rather than MULTIPLY BIG and MULTIPLY SMALL.) (C) Positive evidence approach bias is revealed by subtracting the MUTLIPLY SMALL condition from the MULTIPLY BIG condition. Subjects are more likely to guess early if they have seen evidence that supports them approaching row A rather than avoiding it. This effect is strengthened in AB trials, in which subjects only have the opportunity to sample further information about row B. See also S2 Fig and S3 Fig for other conditions. Data for reproducing all analyses is freely available for download from Dryad.
Fig 3.
Rejecting unsampled option bias at the Choice Stage.
If subjects choose to guess at Task Stage 1, they then select between row A and row B. (A) Model predictions. The relative expected value (in points) of choosing row A versus row B in the ADD BIG (cyan) and ADD SMALL (purple) conditions. Crucially, the decision is identical for AA and AB trials; the only difference between these conditions is which row subjects have previously declined to sample. (B) Subject behavior. The probability of choosing row A shows a softmax relationship to the relative values shown in Fig 3A. Note that the green line (AB trials) is higher than the blue line (AA trials) at nearly all card values, particularly near the point of subjective equivalence. (C) Rejecting unsampled option bias is revealed by subtracting AB trials from AA trials in both ADD BIG and ADD SMALL conditions. Subjects are more likely to choose row A if they have declined to sample row B. See also S4 Fig and S5 Fig for other conditions. Data for reproducing all analyses is freely available for download from Dryad.
Fig 4.
Sampling the favorite bias at Task Stage 2.
If subjects choose to sample at Task Stage 1, they enter Task Stage 2. If this is on an AB trial, they then may sample again from row A, or from row B, or make a guess. (A) Model predictions. The relative expected value (in points) of sampling from row A versus sampling from row B in the MULTIPLY conditions. It is generally more valuable to sample from the row that currently has the higher-valued card (e.g., the 7, in the example shown). Crucially, this prediction is the same in both MULTIPLY BIG and MULTIPLY SMALL conditions. (B) Subject behavior. Subjects show a propensity to sample from the row containing the high-valued card in MULTIPLY BIG, but this trend is reversed in MULTIPLY SMALL. Subjects are therefore inclined to sample the option that is currently most likely to be approached. (C) Sampling the favorite bias is revealed by subtracting MULTIPLY SMALL trials from MULTIPLY BIG trials. The normative model predicts this heat map to show no difference between conditions, yet there is a clear tendency to sample the currently favored row. See also S6 Fig and S7 Fig for other conditions, and S8 Fig for relative value of guessing versus sampling across all six conditions. Data for reproducing all analyses is freely available for download from Dryad.
Fig 5.
Behavioral predictions from the full parametric model of subject behavior, with best-fit parameters.
(A) Predicted probability of guessing at stage 1 for AA trials (compare to Fig 2Bi) and (B) AB trials (compare to Fig 2Bii) in “add” condition. (C) Predicted “positive evidence approach” bias. Compare to Fig 2C. (D) Predicted probability of choosing row A, having chosen to guess, at stage 1, for “add big” (compare to Fig 3Bi) and (E) “add small” (compare to Fig 3Bii) conditions. (F) Predicted “rejecting unsampled options” bias. Compare to Fig 3C. (G) Predicted probability of sampling row A in “big” (compare to Fig 4Bi) and in (H) “small” (compare to Fig 4Bii) conditions. (I) Predicted “sampling the favorite” bias. Compare to Fig 4C. See also S9 Fig. Data for reproducing all analyses is freely available for download from Dryad.
Fig 6.
Expression of all three biases is differentially present in subjects with high versus low Pavlovian approach, quantified in a separate gambling task.
Blue bars denote subjects with below-median values for βgain–βloss; red bars denote subjects with above-median values. (A) The positive evidence approach bias is quantified using the β5 parameter in the parametric model of subject behavior; in both conditions, subjects with high approach-avoid parameter differences show more positive evidence approach than subjects with low parameter differences. (B) The rejecting unsampled option is quantified using the β4 parameter in the parametric model of subject behavior; in the add conditions, there is considerably greater expression of rejecting unsampled option in subjects with high approach-avoid parameter differences; there is a weaker trend in the opposite direction in the multiply condition. (C) The sampling the favorite bias is by quantified using the β6 parameter in the parametric model of subject behavior; in both conditions, subjects with high approach-avoid parameter differences show more sampling the favorite bias than subjects with low parameter differences. Bars/error bars reflect mean/standard deviation across 1,000 bootstrapped samples of 10,000 gameplays. Data for reproducing all analyses is freely available for download from Dryad.
Fig 7.
Individual differences in information seeking.
(A) Histogram of the mean number of cards sampled in each trial relative to how many would be sampled by the optimal model. Subjects show a propensity to guess early, but there is considerable individual variation. (B) Individual variation in information sampling reproduces across subsequent gameplays. Each dot is a subject; subjects who were inclined to seek little information in gameplay 1 also sought little information in gameplay 2. (C) Variation in information seeking (top) and subject performance (bottom) as a function of educational attainment (left panels) and age (right panels). General Certificate of Secondary Education (GCSE) is equivalent to 10th grade in United States; A Level (ALev) is equivalent to 12th grade. Datapoints denote mean +/- standard error of the mean. Data for reproducing all analyses is freely available for download from Dryad.