Biased sequential sampling underlies the effects of time pressure and delay in social decision making

Social decision making involves balancing conflicts between selfishness and pro-sociality. The cognitive processes underlying such decisions are not well understood, with some arguing for a single comparison process, while others argue for dual processes (one intuitive and one deliberative). Here, we propose a way to reconcile these two opposing frameworks. We argue that behavior attributed to intuition can instead be seen as a starting point bias of a sequential sampling model (SSM) process, analogous to a prior in a Bayesian framework. Using mini-dictator games in which subjects make binary decisions about how to allocate money between themselves and another participant, we find that pro-social subjects become more pro-social under time pressure and less pro-social under time delay, while selfish subjects do the opposite. Our findings help reconcile the conflicting results concerning the cognitive processes of social decision making and highlight the importance of modeling the dynamics of the choice process.


Supplementary Methods
Experiment. How to enforce time constraints in this experiment is an important problem. We chose to allow subjects to respond at any time, to avoid missing observations. However, if the timeconstraint was disobeyed, we imposed a probabilistic penalty such that a dictator's decision was only implemented with a probability of 10%. In the other 90% of cases, the dictator earned 0 and the receiver earned the lower of the two amounts that she could earn in the current game. We chose this scheme relying on IIA (independence of irrelevant alternatives) to ensure that subjects would not choose a different option outside of the time constraints and trying to minimize the chance that subjects would prefer the penalized outcome (i.e. worst possible outcome for self, worst available outcome for the other). Subjects were notified with a warning message if they were too slow under time pressure or too fast under time delay (Supplementary Figure 1).
To make sure subjects understood their task, we provided a set of control questions at the beginning of each of the first three parts. In the experiment, we randomly displayed the selfish option and the pro-social option on the left and right sides of the display. We also randomized the display positions (upper or lower) of the dictator's payoffs and the receiver's payoffs across subjects.
Subjects made decisions by pressing the "F" or "J" keys to select the left or right option, respectively.
They saw a waiting screen after each decision and were required to press "Spacebar" to advance to the next trial. At the end of the experiment, we randomly selected one trial for each group and paid them according to one of their decisions (randomly selected). We programed the experiment using z-Tree 1 and recruited subjects via ORSEE 2 . The experimental instructions are as follows.

Supplementary Notes
Supplementary Note 1. Consistent with prior work in this literature 3,4 , our subjects generally did care about both players' payoffs. In the experiment, subjects chose the selfish option in 42.3% of all games in the time-free condition, they chose the selfish option in 50.7% of all games in the time-

Supplementary Note 2.
In addition to using the median indifference , we also considered three other cutoffs to delineate between selfish and pro-social subjects. One is the median subject-level . .
The median subject-level . in our experiment was 0.288. Using this cutoff, 73% of the selfish subjects chose the selfish option on the majority of trials, while 100% of the pro-social subjects chose the prosocial option on the majority of trials. With this cutoff, the pro-social subjects (n=51) become more pro-social under time pressure (P = 0.051, two-sided Wilcoxon signed-rank test, since is not normally distributed), while selfish subjects (n=51) become marginally more selfish under time pressure (P = 0.221). Similarly, pro-social subjects become less pro-social under time delay (P = 0.054), while selfish subjects become less selfish under time delay (P = 0.001).
The second cutoff is the average reported in Fehr & Schmidt (1999). The reported in Fehr & Schmidt (1999) was 0.315. With this cutoff, 67% of the selfish subjects chose the selfish option on the majority of trials; while 100% of the pro-social subjects chose the pro-social option on the majority of trials. With this cutoff, pro-social subjects (n=47) become more pro-social under time pressure (P = 0.024, two-sided Wilcoxon signed-rank test), while selfish subjects (n=55) become marginally more selfish under time pressure (P = 0.098). Similarly, pro-social subjects become less pro-social under time delay (P = 0.052), while selfish subjects become less selfish under time delay

Supplementary Note 3.
To ensure that the biases in starting point were not driven by the selfish (pro-social) behavior of subjects, we simulated a selfish subject with a starting point 0.5 and a drift rate of 0.6. In these simulations, 85.4% of all decisions were selfish decisions. Then we estimated the biased DDM based on the simulated data. We recovered a starting point of 0.484. Therefore, selfish (pro-social) preferences do not appear to produce starting point biases.
To check whether the biases in starting points might have been caused by unaccounted for variability across subjects, we simulated ten selfish subjects with a starting point 0.5 and drift rates 0.1 to 1 in step of 0.1. In the simulations, 79.7% of all decisions were selfish decisions. We then estimate the biased DDM at the group level based on the simulated data. We recovered a starting point of 0.502. Therefore, drift rate variability across subjects does not appear to produce startingpoint biases. For display purpose, (a) includes 69 subjects whose . , / , and 6 are between -1 and 2, (b) includes 71 subjects whose . and / are between -1 and 2, and (c) includes 88 subjects whose . and 6 are between -1 and 2. (a) plots the correlation between the starting point and / − . , and (b) plots the correlation between the starting point and . − 6 . For display purpose, (a) includes 71 subjects whose / and . is between -1 and 2, and (b) includes 88 subjects whose . and 6 is between -1 and 2.

Supplementary Tables
Supplementary Table 1 The dependent variable is a dummy which indicates whether the subject became more pro-social ( 1: / > . or 6 > . ) or selfish ( 0: / < . or 6 < . ) compared to the time-free condition. The independent variable Pro-social is a dummy which indicates whether the subject is prosocial or selfish (split according to the median indifference ). Pressure is a dummy which indicates whether the time condition is time pressure or time delay. ***P < 0.005, **P < 0.01, *P < 0.05. In the OLS regression, the dependent variable is / − 6 . In the Logit regression, the dependent variable is a dummy which indicates whether / > 6 (1) or / < 6 (0). 33 subjects whose . , / , or 6 are outside of [-1, 2] are not included in the OLS regression. 12 subjects whose . are outside of [-1, 2] are not included in the Logit regression. ***P < 0.005, **P < 0.01, *P < 0.05. In OLS regressions, the dependent variable is / − . , . − 6 , or / − 6 . In Logit regressions, the dependent variable is a dummy which indicates whether / > . (1) or / < . (0) under time pressure, whether . > 6 (1) or . < 6 (0) under time delay, and whether / > 6 (1) or / < 6 (0) across timepressure and time-delay conditions. 33 subjects whose / , . , and 6 are outside of [-1, 2] are not included in the OLS regressions. 12 subjects whose . are outside of [-1, 2] are not included in the Logit regressions. ***P < 0.005, **P < 0.01, *P < 0.05.  Notes: The starting points of pro-socially predisposed subjects are significantly less than those of selfishly predisposed subjects (P < 0.001, one-sided Mann-Whitney U test). The thresholds of pro-socially predisposed subjects are significantly higher than those of selfishly predisposed subjects (P < 0.001). The non-decision times of pro-socially predisposed subjects are not significantly different from those of selfishly predisposed subjects (P = 0.933, two-sided Mann-Whitney U test). The parameter S of selfishly predisposed subjects is significantly less than that of pro-socially predisposed subjects (P = 0.027, one-sided Mann-Whitney U test). The parameter Supplementary   Notes: The thresholds of pro-socially predisposed subjects are significantly higher than those of selfishly predisposed subjects (P = 0.002, one-sided Mann-Whitney U test). The non-decision times of pro-socially predisposed subjects are not significantly different from those of selfishly predisposed subjects (P = 0.635, twosided Mann-Whitney U test). The parameter S of pro-socially predisposed subjects is significantly less than that of selfishly predisposed subjects (P = 0.001, one-sided Mann-Whitney U test). The parameter 6 of prosocially predisposed subjects is significantly less than that of selfishly predisposed subjects (P = 0.030). The parameter T of pro-socially predisposed subjects is significantly greater than that of selfishly predisposed subjects (P = 0.022).

Supplementary
Supplementary The dependent variable is a dummy variable which indicates whether the choice is selfish (1) or prosocial (0). The independent variables are the difference between the dictator's payoffs (DicDiff), the difference between the receiver's payoffs (ReceDiff), and the response time (RT). The models are estimated for selfishly predisposed and pro-socially predisposed subjects separately. The robust standard errors are clustered on each subject and reported in parentheses. ***P < 0.005, **P < 0.01, *P < 0.05.