a) Task Overview. Our main task consists of 3 phases. In the Baseline Phase participants acted as a Receiver, responding to offers of different inequity level and rated their perceived fairness towards the offers on three out of every five trials. While, in the subsequent Learning Phase, participants acted as an Agent, deciding on behalf of the Receiver (Teacher) and Proposer. Again, they rated the fairness on three out of every five trials. Finally, participants made choices in a Transfer Phase which was identical to the Baseline Phase. b) Preferences and Fairness Ratings governing the Teacher’s feedback in the Learning Phase (See Table S1 and Table S2). c) Baseline and Transfer phase, in which participants played the Ultimatum game as a Receiver, making choices on their own behalf. dIn the Learning phase, participants acted as a third party (the agent), making decisions on behalf of the Proposer and the Receiver (Teacher), playing a Vicarious Ultimatum game. In a Vicarious Ultimatum game, the Agent make decisions for the Receiver, if he/she rejects the proposed split, both the Proposer and the Receiver receive nothing. If he/she accepts, the Proposer and the Receiver are rewarded with the proposed split.

Behavioral Contagion in Experiment 1

a) Rejection rates change significantly in DI offers for all conditions, while changes in AI offers were only evident in AI-DI-Averse Condition. b) Observing the Teacher’s ratings of AI offers changed fairness ratings in all offer types, while the Teacher’s behaviors in DI offers didn’t. Dashed lines indicate behaviors of the Teacher. Error bars indicate standard error. (†indicates p<0.1, *indicates p<0.05, **indicates p<0.01,***indicates p<0.001)

Learning phase behavior in Experiment 1.

a) Rejection rate changes in Learning Phase. Rejection choices were summarized across participants. For DI Offers, rejection rate increased in both Conditions during learning. While rejection rate only changed (increase) in AI-DI-Averse Condition for AI offers. Sold thin lines denote participants’ rejection choices, dashed lines denote the Teacher’s preferences, and solid thick lines represent predictions of the (bestfitting) Preference Inference Model. b) Model comparison, demonstrating that the Preference Inference model provided the best fit to participant’ Learning Phase behavior (AIC: Akaike Information Criterion) c) and d) Parameters updating for the Preference Inference model. The Preference Inference model captured significant rejection rate increasing in AI offers by updating the guilt parameter in a trial by trial manner.

Relationship between learning and contagion effects in Experiment 1.

Rejection rate changes in Learning phase was indexed by the averaged rejection rate difference between first five and the last five trials in Learning phase. On the DI side, the learning index can predict contagion in both AI-DI-Averse and DI-Averse conditions. while on the AI side, this effect is more salient in the AI-DI-Averse Condition than that in the DI-Averse Condition (†indicates p<0.1, *indicates p<0.05, **indicates p<0.01,***indicates p<0.001)

Baseline and Transfer Phase Behavior in Experiment 2.

a) Contagion in extremely unfair offers. Though no feedback was provided in the Learning phase for 90:10 or 10:90 splits, we observed generalization of punishment preferences in these types of offers. Dashed lines represent the Teacher’s preferences. b) Fairness rating changes. We found significant changes from Baseline to Transfer phase in fairness rating for 90:10 in both AI-DI-Averse and DI-Averse Condition, but only in AI-DI-Averse Condition for 10:90 offers. Error bars represent standard errors (†indicates p<0.1, *indicates p<0.05, **indicates p<0.01,***indicates p<0.001)

Learning Phase Choice Behavior in Experiment 2.

Learning effect were documentedin Extremely unfair offers. Rejection choices were summarized across subjects. Dashed lines indicate Rejection choice of the Teacher. The learning effect were evident for 90:10 offers in DI-Averse condition and 10:90 offers in AI-DI Averse condition. Thin solid lines represnts participants’ rejection choice, thick solid lines show the predictions of the Preference Inference Model , and the dashed lines indicate the Teacher’s preferences (not observed by participants in 90:10 and 10:90 splits).

Model comparison results in Experiment 2. a) AICs of the models considered in experiment 2. b),c). Updating of the ‘guilt’ and ‘envy’ parameters indicates the sanity of the Preference Inference model.

In Experiment 2, Rejection rates changes in the learning phase (indexed by the rejection rate difference between the first and the last five trials in each offer type) predict the rejection rate change from baseline to transfer phase (the contagion).

Reinforcement rates governing the Teacher’s feedback in the Learning Phase. For example, a rate 90% for 90:10 offers indicates that on 90% of trials with that offer type, the Teacher indicated they would have preferred rejection of that offer.

Fairness rating of the Teacher in the Learning Phase in Experiment 1. The teacher rated 90:10 offers as Strongly unfair (1) or Unfair (2) randomly in both conditions.

Baseline Phase Choice Behavior in Experiment 1. Linear mixed model coefficients (fixed effects) indicating effects of condition and Offer type on the baseline Rejection rate.

Baseline Phase Rating Behavior in Experiment 1. Linear mixed model coefficients (fixed effects) indicating effects of condition and Offer type on the baseline Fairness Ratings (testing if the coefficient is equal to 4).

Contagion effects in rejection rates in Experiment 1, computed as the difference between Transfer and Learning Phase rejection rates. Linear mixed model coefficients (fixed effects) indicating the effects of Condition and Offer Type on the Rejection rate changes from Baseline to Transfer phase.

Contagion effects in Fairness ratings in Experiment 1, computed as the difference between Transfer and Learning Phase fairness ratings. Linear mixed model coefficients (fixed effects) indicating the effects of Condition and Offer Type on the Fairness rating changes.

Mixed-effects logistic regression examining Rejection choices (Reject vs. Accept) during the Learning Phase in Experiment 1, as a function of the interactions between Condition, Offer Type, and Trial Number.

Summary of Model Comparison in Experiment 1.

Relationships between Learning Phase Behavior and Contagion in Experiment 1. Linear Mixed model coefficients (fixed effects) indicating the effects of Condition, Offer Type, and Learning index (Rejection rate change between first and last five trials of Learning phase) on the Contagion effect (Rejection rate changes from Baseline to Transfer phase).

Contagion effects in Experiment 2. Linear mixed model coefficients (fixed effects) indicating the effects of Condition and Offer Type on the Rejection rate changes (from Baseline phase to Transfer phase).

Contagion effect of Fairness rating in Experiment 2. Linear mixed model coefficients (fixed effects) indicating the effects of Condition and Offer Type on the Fairness rating changes from Baseline to Transfer phase.

Mixed-effects logistic regression examining Rejection choices (Reject vs. Accept) during the Learning Phase in Experiment 2, as a function of the interactions between Condition, Offer Type, and Trial Number.

Mixed-effects regression examining Fairness ratings during the Learning Phase in Experiment 2, as a function of the interactions between Condition, Offer Type, and Trial Number.

Summary of Model Comparison in Experiment 2.