Food-choice task.

The task consisted of two phases. In the first phase (A), participants were shown 70 pictures of snack items, one at a time, and were asked to rate how much they would like to consume each item on a scale from -10 to 10. In the second phase (B), participants were presented with pairs of items that had received non-negative ratings in the first phase and were asked to choose which item they preferred. Before the snack items were presented, participants had to fixate on a central marker for 2 seconds. To report their choice, participants used the left and right arrows on a keyboard. After the choice report, the items were displayed for an additional second, during which time the selected item was highlighted. Each of the 39 participants completed 100 trials. (C) Gaze allocation between the left and right items shown from the moment both snacks appeared on the screen, for 11 representative trials. Red and blue indicate gaze directed to the left and right items, respectively. Times when the gaze was not directed to either item are left blank. Black dots indicate the time when the left or right key was pressed.

Magnitude effect on last-fixation bias.

(top) Influence on choice of the gaze right before the choice report, as measured with logistic regression (Eq. 3), as a function of the sum of the ratings assigned to of the left and right item (‘overall’ value or Σr). The five data points correspond to quintiles of the data, split by Σr. The dashed line is obtained from a related regression model that includes an interaction term between Σr and whether the last fixation was on the ultimately chosen item or on the unchosen item before the report. Error bars are s.e. The p-value indicated in each panel corresponds to a test of the hypothesis that the slope of the dashed line is equal to zero, evaluated using the z-test. (bottom) Proportion of trials for which participants (or the simulations) chose the item looked at last, as a function of the difference in value between the item looked at last and the other item. Trials were median-split by Σr. The choice functions were calculated per participant and then averaged across participants. Error bars are s.e.m. across participants. The four panels correspond to (A) simulations of the aDDM, (B) behavioral data from Krajbich et al. (2010), (C) Callaway et al’s model (2021), and (D) Jang et al’s model (2021).

Difference in looking time for consistent and inconsistent choices.

Time spent looking at the chosen item minus time spent looking at the unchosen item, as a function of response time. The four panels correspond to (A) simulations of the aDDM, (B) behavioral data from Krajbich et al. (2010), (C) Callaway et al’s model, and (D) Jang et al’s model. For each participant, we grouped trials into 20 categories defined by the response time decile and the consistency of the choice with the initial rating. Trials in which the two items were assigned the same value during the rating phase were excluded from the analysis, as the choices cannot be classified neither as consistent nor inconsistent. The response times shown on the abscissa correspond to the mean response times (across participants) for the corresponding decile. Error bars are s.e.m. across participants.

Sketch of the PDG model.

(A) The decision is generated by accumulating momentary evidence over time until the process reaches either an upper or lower bound. Evidence accumulation begins after a sensory delay, τs. Once a bound is crossed, an additional motor delay, τm, elapses before the manual response is executed. Thus, the response time equals the decision time plus the non-decision delays τs and τm. Gaze does not affect the decision process. Instead, at a random latency τe after the bound crossing, the gaze is directed toward the chosen option and remains there until the manual response. Because τe is typically shorter than τm, the chosen item is usually the last fixated item before the response. (B) Example simulation in which the gaze is already on the chosen item at time τe following bound crossing; therefore, no gaze shift occurs. (C) Simulation in which the gaze shift to the chosen item occurs only after the manual response, and therefore does not influence pre-response gaze behavior. This explains why, in some trials—including the example shown—the non-chosen item is the last one fixated before the response.

Human behavior and fits of the PDG model.

(A) Proportion of trials in which the right item was selected as a function of the difference in value between the right and left items (Δr). Points represent behavioral data and shading represents model fits. (B) Proportion of trials in which the right item was selected, separated by whether the last fixation before the report was on the left (purple) or the right (green) item. (C) Mean response time as a function of the value difference between the two items. (D) Residual response time (after subtracting the contribution of Δr) as a function of the sum of the value of the two items presented in the trial (Σr). Error bars indicate standard error of the mean (s.e.m.) across trials. (E) Probability that the decision maker is looking at the item that was ultimately chosen, plotted relative to the time since the two items were presented on the screen (left) and the response time (right). Error bands indicate 95% confidence intervals for the mean across participants. In the stimulus-aligned plot, the data are shown from the first moment that one of the two items is fixated on in at least 50% of the trials, which is ∼0.25 s. (F) MELFB for data (black) and model (orange). Same conventions as in Fig. 2. (G) Gaze bias for consistent and inconsistent choices. Same conventions as in Fig. 3. (H) Proportion of trials in which the left item was selected as a function of the difference in dwell time between the left and right items. Data (black) and model (orange) were grouped in deciles of the dwell difference, separately for each participant, and then averaged across participants. (I) Proportion of trials in which the item looked at first was selected, as a function of duration of the first dwell. Data (black) and model (orange) were grouped in deciles of the first dwell duration, separately for each participant, and then averaged across participants. In all panels except panel B and G, data are shown in black and model simulations are shown in orange. Error bars and error bands, unless otherwise noted, show the standard error of the mean (s.e.m.) across participants (N=39 for both model and data).

Gaze allocation after the choice report.

(A) Probability that the decision maker is looking at the item that was ultimately chosen, aligned to RT. This probability increases even after the choice report. Error bands indicate 95% confidence intervals for the mean across participants. (B) Proportion of time that the decision maker is looking at the item that was ultimately chosen, calculated for the last 200 ms before the response (abscissa) and for the first 200 ms after the response (ordinate). Each data point represents one participant. Proportions were calculated as the sum of the time spent looking at the chosen item divided by the time spent looking at either one of the items (i.e., we exclude the times when the gaze was not directed at one of the two items).

Association between first-dwell duration and choice probability.

(A) Model-predicted probability of choosing the option that was fixated first, as a function of the duration of the first dwell. Trials are grouped by the total number of dwells (2–5), shown in separate colors. Data were binned into quartiles of first-dwell duration and then averaged across participants. Error bars indicate s.e.m. (B) Same analysis as A, for the behavioral data.

Human behavior and fits of the aDDM

Same conventions as in Fig. 5. In panel E, only periods during which the participant is fixating one of the two items are included, as the drift rate in the aDDM is undefined otherwise. Accordingly, the plot shows time relative to fixation (i.e., elapsed fixation time), rather than absolute elapsed time as in Fig. 5.

Human behavior and fits of a model with additive intra-decisional attention.

Same conventions as in Fig. 8.

Human behavior and simulations of the combined aDDM and PDG model.

Starting from the aDDM simulations in Fig. 8, we added two features from the PDG model: (i) a gaze shift to the chosen item occurring with a delay τe after bound crossing, and (ii) a sensory delay τs between stimulus onset and the start of evidence accumulation. Same conventions as in Fig. 5.

Model with intra- and post-decisional attentional effects, and inter-trial variability in the drift-rate.

Same as Fig. 10 but adding inter-trial variability in the drift-rate across trials. Same conventions as in Fig. 5.

Difference in looking time for consistent and inconsistent choices in other datasets.

Same analysis as shown in Fig. 3, for six additional datasets. Each panel shows the difference in looking time between the chosen and the unchosen item (ΔDwell), as a function of response time, computed separately for choices that were consistent and inconsistent with stated valuation. The corresponding dataset is indicated in each panel. In Sepulveda et al. (2020), participants either selected the item they preferred or the one they did not prefer. We analyzed the two variants separately. Plotting conventions match those in Fig. 3.

Removing the contribution of Δr from response times.

Illustration of the method used to remove the contribution of Δr from the RT. The gray markers indicate the RT for each trial of a representative participant. The abscissa are the values of Δr for the corresponding trial. These data points were fitted with the bell-shaped function shown in the figure, with parameters a, b, μ and σ. The best-fitting function captures the general trend in the data, as can be seen by comparing the model fits (black solid line) with the average response time per value of Δr (red, mean plus s.e.m.). To compute the RT residuals, we subtract from each trial the value of R^T corresponding to the corresponding value of Δr. Fits were performed independently for each participant.

Fits of the duration of the dwells.

Distribution of the durations of the first dwell (left) and middle dwells (right). Middle dwells include all dwells except the first and last. The durations were fitted with a log-normal distribution (red), independently for the first and middle dwells. The best-fitting log-normal parameters were used to simulate the aDDM and gDDM. On each trial, the first dwell is sampled from the corresponding distribution, and the subsequent dwell durations up to the bound crossing are sampled from the distribution of middle dwells.

Parameter recovery for the aDDM.

For each participant, we simulated choices and decision times using their individually best-fitting model parameters, with the same number of trials as in the original experiment. Each panel shows, for a given model parameter, the value estimated from the empirical data (x-axis) plotted against the corresponding value recovered from the simulated data (y-axis). Each point represents one participant (N=39).

Parameter recovery for the aDDM variant with additive attention.

Same as Fig. S3, for the model in which the effect of attention on choice is additive rather than multiplicative.

Relative goodness-of-fit of the additive and multiplicative models.

Difference in Bayesian Information Criterion (ΔBIC) between models with multiplicative and additive attention effects. Positive values indicate support for the additive model. Overall, both models achieved comparable goodness-of-fit.

Model with intra-decisional attentional effects and inter-trial variability in the drift-rate.

Same as Fig. 8 but including inter-trial variability in the drift-rate across trials. Same conventions as in Fig. 5.

aDDM model.

Model simulations were generated using the aDDM with the best-fitting parameters reported by Krajbich et al. (2010) and Smith and Krajbich (2019). This version of the model assumes constant (i.e., flat) decision bounds and no inter-trial variability in drift rate. Unlike the models presented in the main text, it was fit by Krajbich et al. (2010) to data pooled across participants. Same conventions as in Fig. 5.

Model with intra- and post-decisional attention, and inter-trial variability in the items’ value.

Unlike the model illustrated in Fig. 11, here the items’ values—instead of the drift rates—are corrupted with additive Gaussian noise. This noise is fixed within each trial but varies randomly across trials. Model parameters were fit to individual participants’ choice, RT, and fixation data. Same conventions as in Fig. 5.

Model of Callaway et al. (2021).

Model simulations were obtained from the approximately optimal model of Callaway et al. (2021). Same conventions as in Fig. 5.

Model of Jang et al. (2021).

Model simulations were generated with the optimal model of Jang et al. (2021). Same conventions as in Fig. 5.

Best-fitting parameter values for the PDG model.

Best-fitting parameter values for the aDDM.

Best-fitting parameter values for the model with additive intra-decision attention.

Best-fitting parameter values for the aDDM with inter-trial drift-rate variability.