Standard models of law enforcement involve the apprehension and punishment of a single suspect, but in many contexts, punishment is actually imposed on an entire group known to contain the offender. The advantages of .group punishment. are that the offender is punished with certainty and detection costs are saved. The disadvantage is that innocent individuals are punished. We compare individual and group punishment when social welfare depends on fairness, and when it depends on deterrence. We show that group punishment may dominate in the former case if the detection technology is ineffective but never in the latter case. We discuss our results in the context of several examples.