Justice systems delegate punishment decisions to groups in the belief that the aggregation of individuals' preferences facilitates judiciousness. However, group dynamics may also lead individuals to relinquish moral responsibility by conforming to the majority's preference for punishment. Across five experiments (N = 399), we find Victims and Jurors tasked with restoring justice become increasingly punitive (by as much as 40%) as groups express a desire to punish, with every additional punisher augmenting an individual's punishment rates. This influence is so potent that knowing about a past group's preference continues swaying decisions even when they cannot affect present outcomes. Using computational models of decision-making, we test long-standing theories of how groups influence choice. We find groups induce conformity by making individuals less cautious and more impulsive, and by amplifying the value of punishment. However, compared to Victims, Jurors are more sensitive to moral violation severity and less readily swayed by the group. Conformity to a group's punitive preference also extends to weightier moral violations such as assault and theft. Our results demonstrate that groups can powerfully shift an individual's punitive preference across a variety of contexts, while additionally revealing the cognitive mechanisms by which social influence alters moral values.