Figures and data
a) Task Overview. Our main task consists of three 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. d) In the Learning phase, participants acted as a third party (the agent), making decisions on behalf of the Proposer and the Receiver (Teacher), playing a Third-Party Ultimatum game. In a Third-Party 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 as the proposed split.
Behavioral Contagion in Experiment 1
a) Rejection rates change significantly in Dis-I offers for all conditions, while changes in Adv-I offers were only evident in Adv-Dis-I-Averse Condition. Importantly, this change in Adv-I Offers differs between conditions, indicating a contagion effect. b) Observing the Teacher’s ratings of Adv-I offers changed fairness ratings in all offer types, while observing the Teacher’s behaviors in Dis-I offers didn’t. Similarly, fairness rating changes in Adv-I offers are different between conditions. 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, x indicates interaction)
Learning phase behavior in Experiment 1.
a) Rejection rate changes in Learning Phase. Rejection choices were summarized across participants. For Dis-I Offers, rejection rate increased in both Conditions during learning. While the rejection rate only changed (increased) in the Adv-Dis-I-Averse Condition for AI offers. Furthermore, in Adv-I offers, the increasing trend was larger in the Adv-Dis-I-Averse condition than in the Dis-I-averse condition, indicating a learning effect. Solid thin lines denote participants’ rejection choices, dashed lines denote the Teacher’s preferences, and solid thick lines represent predictions of the (best-fitting) Preference Inference Model. b) Model comparison, demonstrating that the Preference Inference model provided the best fit to participants’ Learning Phase behavior (AIC: Akaike Information Criterion) c) and d) Parameters updating for the Preference Inference model. The Preference Inference model captured a significant rejection rate increase in Adv-I offers by updating the guilt parameter in a trial-by-trial manner.
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 Adv-Dis-I-Averse and Dis-I-Averse Condition, but only in Adv-Dis-I-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 effects were documented in extremely unfair offers. Rejection choices were summarized across subjects. Dashed lines indicate the Rejection choice of the Teacher. The learning effect was evident for 90:10 offers in Dis-I-Averse condition and 10:90 offers in Adv-Dis-I Averse condition. Thin solid lines represent 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.
Model recovery results for the Preference Inference model.
All parameters are recoverable. Though the correlation between the true value and the recovered value of the inverse temperature is relatively low.
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.
Model:
RejectionRate ~ 0 + (DisI + AdvDisI). (Offer10 + Offer30 + Offer50 + Offer70 + Offer90) + (1|Subject)
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). The models are the same as in Table S3, except for that the dependent variable is the fairness rating.
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. The model is the same as in Table S3, except for that the dependent variable is rejection rates changes from baseline to transfer.
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. The model is the same as in Table S3, except for that the dependent variable is the fairness rating changes from baseline to transfer.
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.
Model:
Rejection Choice ~ (AdvDisI + DisI): (Offer10 + Offer 30 + Offer50 + Offer70 + Offer90) * ZTrial − ZTrial − 1 + ((Offer10 + Offer30 + Offer50 + Offer70 + Offer90) *ZTrial − 1 − ZTrial||Subject)
Summary of Model Comparison in Experiment 1.
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). This model specification is identical to that used in Experiment 1 (reported in in Table S3).
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. The model is the same as in Table S4
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.
The model is the same as in Table S7.
