Supplementary Figure 7: Probabilistic nature of outcomes.

The 80% probability of implementation was introduced to the Choice condition to equalize the approximate payoff considerations across the two conditions, as message receivers typically follow received messages about 80% of the time, according to both our data as well previous research². A possible concern arises in that it may have had the additional consequence of giving participants some plausible deniability, or an "out", in the Choice condition that is not present in the Message condition, which could have contributed to participants' greater selfishness in the Choice condition. To investigate this, we conducted an additional study on Amazon’s Mechanical Turk in which we manipulated this factor directly using a 2 (condition: Choice, Message) x 2 (probability of implementation: 80%, 100%) design. In particular, we introduced plausible deniability into the Message condition by telling participants, "When you choose a message, there is an 80% chance that it will be delivered to the other person. There is a 20% chance that the other message will be delivered" (Message-80%) versus "When you choose a message, it will be delivered to the other person" (Message-100%). Similarly, we removed plausible deniability from the Choice condition by telling participants, "When you choose an option, it will be implemented" (Choice-100%) versus "When you choose an option, there is an 80% chance that it will be implemented. There is a 20% chance that the other choice will be implemented" (Choice-80%). We ran this study in a between-subjects design (n=163) in which each participant made a single decision in one of the four conditions. Consistent with our previous results, a two-way ANOVA revealed a significant reduction in selfish choices in the Message condition relative to the Choice condition (F(1,159)=32.98,p<.0001), which was present across both levels of probability (t-tests, p < 0.006 for each). Moreover, we found that decisions were not significantly affected by the probability of implementation (F(1,159)=1.86,p>.17), and there was no significant interaction between condition and probability (F(1,159)=0.43,p>.83). We observed significantly fewer selfish choices in the Message condition relative to the Choice condition across both the 80% (t(74)=5.31,p<.0001) and 100% (t(89)=2.86,p<.005) implementation probabilities. Thus, although we cannot rule out that lesion participants held substantially different beliefs regarding the probability of implementation, our results suggest that it is difficult for differences in beliefs to completely explain observed behavioral differences between the Choice and Message conditions. Future studies directly probing beliefs on part of lesion patients will be important to address this question as well as larger question of contribution of theory of mind to honesty and deception.