Abstract Proposals to provide juries with specific numerical instructions for setting punitive damages should bring greater rationality to punitive damages awards. This approach is tested using evidence from 353 jury‐eligible citizens who applied these formulas to a series of legal cases. Few respondents assessed the correct values of punitive damages from the standpoint of deterrence. Anchoring effects of appeals by a plaintiff’s lawyer or media coverage of similar awards lead respondents to abandon the punitive damages formula and set punitive damages based on the anchor. Minorities and the less well educated were particularly unwilling or unable to apply the recommended punitive damages formulas.