Food-choice task

The food-choice paradigm consists of two phases. In the first phase (A), participants were shown pictures of snack food items, one at a time, and were asked to rate how much they would like to consume each item, either on a numerical liking scale (Krajbich et al., 2010; Smith and Krajbich, 2018; Chen and Krajbich, 2016; Gwinn and Krajbich, 2016) or by stating their maximum willingness to pay in an incentive-compatible auction (Folke et al., 2016; Sepulveda et al., 2020). Note that while the original experiments used photographs of real packaged foods, the items depicted here are illustrative mockups. In the second phase (B), participants were presented with pairs of items and asked to choose which one they would prefer to consume at the end of the experiment. Participants responded manually; in most datasets, responses were made using the left and right arrow keys on a keyboard. (C) Gaze allocation between the left and right items shown from the moment both snacks appeared on the screen, for 11 representative trials from Krajbich et al. (2010). 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.

aDDM behavioral predictions

(A)Estimated strength of the association between last-dwell focus and choice (logistic regression coefficient; Eq. 3) as a function of overall value (Σr). The five data points correspond to quintiles of the data, split by Σr. The data were generated from simulations of the aDDM using the parameters reported in (Krajbich et al., 2010) and (Smith and Krajbich, 2019). The dashed line is derived from a related regression model that includes an interaction term between Σr and whether the last fixation before the report was on the ultimately chosen or unchosen item. Error bars indicate s.e. (B)Time spent looking at the chosen item minus time spent looking at the unchosen item, as a function of response time. The data were generated from simulations of the aDDM. For each participant, trials were grouped into 20 categories defined by response-time decile and whether the choice was consistent with the initial ratings. Trials in which the two items received the same rating during the rating phase were excluded, because such choices cannot be classified as either consistent or inconsistent. The response times shown on the abscissa correspond to the mean response time across participants for each decile. Error bars indicate s.e. across participants.

Association strength between last dwell and choice

Estimated strength of the association between last-dwell focus and choice as a function of Σr. Same analysis and conventions as in Fig. 2A. Each panel shows data from a different dataset of the food-choice task: (A) Krajbich et al. (2010), (B) Smith and Krajbich (2018), (C) Chen and Krajbich (2016), (D) Gwinn and Krajbich (2016).

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. Same analysis and conventions as in Fig. 2. The seven panels correspond to behavioral data from (A) Krajbich et al. (2010), (B) Smith and Krajbich (2018), (C) Chen and Krajbich (2016), (D) Gwinn and Krajbich (2016), (E) Folke et al. (2016), (F-G) Sepulveda et al. (2020). 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.

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.

Data from Krajbich et al. (2010) and fits of the PDG model

(A) Proportion of trials in which the left item was selected as a function of the difference in value between the left and right items (Δr). Points represent behavioral data and shading represents model fits. (B) Mean response time as a function of the value difference between the two items. (C) 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. (D) Proportion of trials in which the left item was selected, separated by whether the last fixation before the report was on the right (purple) or the left (green) item. (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. 3. (G) Gaze bias for consistent and inconsistent choices. Same conventions as in Fig. 4. (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 D 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).

Sensitivity of the gaze–choice association in the PDG model

Simulations of the PDG model across a range of eye-movement latency values (μe), assessing the robustness of the model’s predictions. (A) Predicted gaze-cascade effect. Similar analysis to that in Fig. 6E. (B) Predicted association between last-dwell focus and choice. Similar analysis to that in Fig. 6F. (C) Predicted ΔDwell (chosen minus unchosen) for consistent and inconsistent choices as a function of response time. Similar to the analysis in Fig. 6G.

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.

Predictions from different models

Fits of different models to the data of Krajbich et al. (2010). Same analyses and conventions as in Fig. 6. (A) Data and fits of the aDDM model. (B) aDDM with additive instead of multiplicative attention. (C) aDDM with post-decision attention. (D) aDDM with inter-trial variability in the drift-rates. (E) aDDM with inter-trial variability in the drift-rates and post-decision attention. (F) Model from Callaway et al. (2021). (G) Model from Jang et al. (2021).

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 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 PDG. 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.

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. 6.

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

Unlike the model illustrated in Fig. 10D, 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. 6.

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.

Comparison of experimental design features across food choice studies.