Figures and data in Behavioral signatures of post-decisional attention in preferential choice

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Tables
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11 figures, 5 tables and 1 additional file

Figures

Figure 1

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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.

Figure 2

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*aDDM* behavioral predictions.

(A) Estimated strength of the association between last-dwell focus and choice (logistic regression coefficient; Equation 3) as a function of overall value ( $Σ r$ ). The five data points correspond to quintiles of the data, split by $Σ r$ . 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 $Σ r$ 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.

Figure 3

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Association strength between last dwell and choice.

Estimated strength of the association between last-dwell focus and choice as a function of $Σ r$ . Same analysis and conventions as in Figure 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, and (D) Gwinn and Krajbich, 2016.

Figure 4

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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 Figure 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, and (**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.

Figure 5

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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, $τ_{s}$ . Once a bound is crossed, an additional motor delay, $τ_{m}$ , elapses before the manual response is executed. Thus, the response time equals the decision time plus the non-decision delays $τ_{s}$ and $τ_{m}$ . Gaze does not affect the decision process. Instead, at a random latency $τ_{e}$ after the bound crossing, the gaze is directed toward the chosen option and remains there until the manual response. Because $τ_{e}$ is typically shorter than $τ_{m}$ , 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 $τ_{e}$ following bound crossing; therefore, no gaze shift occurs. (C) Due to stochastic variability, $τ_{e} > τ_{m}$ in a subset of trials, causing the post-commitment gaze shift to the chosen item to occur only after the manual response. This explains why, in some trials—including the example shown—the non-chosen item is the last one fixated before the response.

Figure 6 with 2 supplements

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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 ( $Δ r$ ). 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 $Δ r$ ) as a function of the sum of the value of the two items presented in the trial ( $Σ r$ ). 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 Figure 3. (G) Gaze bias for consistent and inconsistent choices. Same conventions as in Figure 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 panels (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).

Figure 6—figure supplement 1

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Removing the contribution of $Δ r$ from response times.

Illustration of the method used to remove the contribution of $Δ r$ from the RT. The gray markers indicate the RT for each trial of a representative participant. The abscissa are the values of $Δ r$ 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 $Δ r$ (red, mean plus s.e.m.). To compute the RT residuals, we subtract from each trial the value of $\hat{R T}$ corresponding to the corresponding value of $Δ r$ . Fits were performed independently for each participant.

Figure 6—figure supplement 2

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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.

Figure 7

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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).

Figure 8

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Sensitivity of the gaze–choice association in the *PDG* model.

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

Figure 9

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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.

Figure 10 with 2 supplements

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Fits of different models to the data of Krajbich et al., 2010.

Same analyses and conventions as in Figure 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.

Figure 10—figure supplement 1

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

Unlike the model illustrated in Figure 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 and RT. Same conventions as in Figure 6.

Figure 10—figure supplement 2

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*aDDM* model simulations 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 no inter-trial variability in drift rate. Unlike the models presented in the main text, this version of the *aDDM* was fit by Krajbich et al., 2010 to data pooled across participants. Same conventions as in Figure 6.

Author response image 1

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Fits of a variant of the MACS model (Gluth et al. 2026) to the data of Krajbich et al. (2010).

Tables

Appendix 1—table 1

Best-fitting parameter values for the PDG model.

Subject	$κ$	$μ_{n d}$	$σ_{n d}$	$B$	$γ$
1	0.369	0.536	0.018	1.293	0.000
2	0.076	0.671	0.091	1.311	0.067
3	0.187	0.600	0.144	2.084	0.000
4	0.216	1.219	0.235	0.999	0.141
5	0.383	0.544	0.010	2.004	0.171
6	0.244	0.886	0.140	0.613	0.000
7	0.197	0.536	0.035	2.116	0.055
8	0.617	1.090	0.143	1.612	0.247
9	0.551	0.702	0.044	1.254	0.137
10	0.292	0.706	0.142	1.483	0.038
11	0.353	0.730	0.012	1.467	0.000
12	0.243	0.525	0.010	1.547	0.000
13	0.242	0.646	0.013	1.707	0.021
14	0.332	0.649	0.011	1.201	0.000
15	0.058	0.598	0.010	2.184	0.233
16	0.335	0.738	0.143	1.065	0.000
17	0.224	0.774	0.010	2.150	0.024
18	0.198	1.498	0.338	1.810	0.021
19	0.459	0.551	0.010	2.487	0.212
20	0.192	0.778	0.163	1.673	0.045
21	0.349	0.523	0.010	2.079	0.296
22	0.425	1.255	0.195	1.298	0.009
23	0.535	0.879	0.108	0.994	0.180
24	0.314	1.225	0.222	1.024	0.061
25	0.348	0.973	0.129	0.888	0.025
26	0.203	0.626	0.017	1.243	0.000
27	0.468	0.538	0.047	0.862	0.145
28	0.057	1.071	0.010	1.150	0.002
29	0.258	0.654	0.023	1.916	0.047
30	0.291	0.680	0.182	1.448	0.000
31	0.363	0.540	0.010	1.438	0.176
32	0.340	0.679	0.017	1.622	0.076
33	0.450	0.880	0.163	0.702	0.000
34	0.439	0.944	0.145	1.110	0.000
35	0.418	0.615	0.086	1.116	0.320
36	0.281	0.735	0.178	1.057	0.095
37	0.066	0.859	0.156	0.866	0.000
38	0.268	0.722	0.014	1.668	0.004
39	0.259	0.662	0.034	1.336	0.007

Appendix 1—table 2

Best-fitting parameter values for the aDDM.

Subject	$κ$	$B$	$θ$
1	0.368	1.433	0.802
2	0.120	1.291	0.262
3	0.219	2.164	0.797
4	0.214	0.625	0.731
5	0.282	1.355	0.500
6	0.186	1.115	1.000
7	0.203	1.930	0.452
8	0.384	1.702	0.202
9	0.427	1.374	0.597
10	0.356	1.731	0.308
11	0.356	1.649	0.786
12	0.227	0.857	1.000
13	0.247	1.550	0.820
14	0.309	1.245	0.827
15	0.100	1.584	0.484
16	0.349	1.388	0.681
17	0.268	2.257	0.546
18	0.205	1.692	0.778
19	0.338	1.832	0.694
20	0.264	1.684	0.219
21	0.258	1.092	0.469
22	0.362	2.090	0.712
23	0.312	1.299	0.733
24	0.416	1.728	0.000
25	0.349	1.547	0.181
26	0.220	1.512	0.783
27	0.334	0.985	0.447
28	0.396	1.782	0.000
29	0.285	1.915	0.384
30	0.387	1.905	0.000
31	0.334	1.407	0.480
32	0.556	1.900	0.000
33	0.368	1.302	0.599
34	0.559	1.629	0.229
35	0.493	1.167	0.099
36	0.236	1.232	0.754
37	0.200	1.373	0.000
38	0.318	2.089	0.557
39	0.378	1.436	0.384

Appendix 1—table 3

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

Subject	$κ$	$B$	$ω$
1	0.334	1.442	1.511
2	0.100	1.294	5.000
3	0.197	2.171	0.700
4	0.185	0.625	0.866
5	0.218	1.338	3.531
6	0.186	1.115	–0.820
7	0.152	1.927	3.584
8	0.285	1.730	5.000
9	0.349	1.399	2.522
10	0.261	1.731	5.000
11	0.320	1.658	1.499
12	0.238	0.858	–0.620
13	0.225	1.545	0.302
14	0.281	1.245	0.869
15	0.100	1.586	0.864
16	0.293	1.430	2.897
17	0.213	2.279	3.123
18	0.183	1.685	1.289
19	0.288	1.830	0.957
20	0.163	1.684	5.000
21	0.195	1.090	4.289
22	0.307	2.099	2.395
23	0.272	1.346	2.682
24	0.249	1.752	5.000
25	0.233	1.577	5.000
26	0.196	1.515	1.241
27	0.238	0.980	2.740
28	0.209	1.716	5.000
29	0.202	1.930	3.166
30	0.272	1.950	5.000
31	0.255	1.457	2.967
32	0.288	1.910	3.207
33	0.283	1.329	3.061
34	0.353	1.635	2.081
35	0.254	1.162	5.000
36	0.207	1.236	1.538
37	0.113	1.308	5.000
38	0.246	2.105	3.384
39	0.257	1.443	1.841

Appendix 1—table 4

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

Subject	$κ$	$B$	$θ$	$σ_{drift}$
1	0.369	1.435	0.803	0.000
2	0.158	1.495	0.405	0.804
3	0.223	2.179	0.799	0.095
4	0.213	0.625	0.727	0.000
5	0.464	1.804	0.576	1.205
6	0.335	1.762	1.000	1.494
7	0.263	2.172	0.532	0.490
8	0.570	2.514	0.224	1.125
9	0.430	1.377	0.596	0.091
10	0.578	2.463	0.415	1.062
11	0.494	2.041	0.791	0.808
12	0.227	0.855	1.000	0.007
13	0.495	2.075	0.877	1.050
14	0.387	1.356	0.868	0.621
15	0.100	1.788	0.634	0.681
16	0.373	1.439	0.678	0.336
17	0.871	5.911	0.590	2.128
18	0.204	1.690	0.778	0.000
19	0.861	3.409	0.669	1.543
20	0.385	2.144	0.293	0.816
21	0.258	1.090	0.468	0.007
22	1.160	6.722	0.721	2.582
23	0.381	1.553	0.772	0.822
24	0.854	3.662	0.000	1.740
25	0.466	2.039	0.235	0.927
26	0.422	2.157	0.803	1.178
27	0.378	1.101	0.477	0.815
28	0.686	2.889	0.000	1.361
29	0.357	2.164	0.443	0.522
30	0.551	2.482	0.000	0.886
31	0.502	1.822	0.563	1.000
32	0.839	2.622	0.114	0.884
33	0.512	1.763	0.641	1.057
34	0.708	1.968	0.301	0.688
35	0.856	1.827	0.260	1.555
36	0.309	1.410	0.778	0.738
37	0.384	2.248	0.000	1.460
38	0.445	2.581	0.604	0.637
39	0.628	1.887	0.447	1.062

Appendix 1—table 5

Comparison of experimental design features across food-choice studies.

Feature	Krajbich et al., 2010	Smith and Krajbich, 2018	Chen and Krajbich, 2016	Gwinn and Krajbich, 2016	Folke et al., 2016	Sepulveda et al., 2020
Number of subjects	39	44	44	36	28	31
Valuation method	Liking (−10/+10)	Liking (−10/+10)	Liking (−10/+10)	Yes/no +liking (0–10)	BDM (£0–£3)	BDM (£0–£3)
Items rated	70	147	139	147	60	60
Max value difference	5	5	3	1	Unconstrained	Unconstrained
Number of trials	100	200	200	200	120	240
Confidence rating	No	No	No	No	Yes	Yes
Task framing	Like only	Like only	Like only	Like only	Like only	Like + dislike
Post-session re-rating	No	No	No	Yes	No	No

Additional files

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Ariel Zylberberg
Ian Krajbich
Michael N Shadlen

(2026)

Behavioral signatures of post-decisional attention in preferential choice

eLife 15:RP110729.

https://doi.org/10.7554/eLife.110729.3

Figures

Food-choice task.

aDDM behavioral predictions.

Association strength between last dwell and choice.

Difference in looking time for consistent and inconsistent choices.

Sketch of the PDG model.

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

Removing the contribution of $Δ r$ from response times.

Fits of the duration of the dwells.

Gaze allocation after the choice report.

Sensitivity of the gaze–choice association in the PDG model.

Association between first-dwell duration and choice probability.

Fits of different models to the data of Krajbich et al., 2010.

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

aDDM model simulations generated using the aDDM with the best-fitting parameters reported by Krajbich et al., 2010 and Smith and Krajbich, 2019.

Fits of a variant of the MACS model (Gluth et al. 2026) to the data of Krajbich et al. (2010).

Tables

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.

Additional files

MDAR checklist

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Food-choice task.

aDDM behavioral predictions.

Association strength between last dwell and choice.

Difference in looking time for consistent and inconsistent choices.

Sketch of the PDG model.

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

Removing the contribution of Δr from response times.

Fits of the duration of the dwells.

Gaze allocation after the choice report.

Sensitivity of the gaze–choice association in the PDG model.

Association between first-dwell duration and choice probability.

Fits of different models to the data of Krajbich et al., 2010.

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

aDDM model simulations generated using the aDDM with the best-fitting parameters reported by Krajbich et al., 2010 and Smith and Krajbich, 2019.

Fits of a variant of the MACS model (Gluth et al. 2026) to the data of Krajbich et al. (2010).

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.

MDAR checklist

Downloads (link to download the article as PDF)

Open citations (links to open the citations from this article in various online reference manager services)

Cite this article (links to download the citations from this article in formats compatible with various reference manager tools)

Removing the contribution of $Δ r$ from response times.