Optimal Punishment Schemes for Impulsive Offenders: The Case for a Reduced Penalty Rule

Abstract This study examines optimal punishment schemes within the economics of crime by introducing offender impulsiveness. Although prior studies have supported the Proportionality Rule, where penalties increase with the severity of crimes in contexts involving multiple criminal opportunities, these models typically assume fully rational offenders. However, recent findings in criminology and behavioral economics suggest that many crimes are impulsive. This study theoretically demonstrates that, within a framework that simultaneously considers multiple offenses and determines the sentence for each, when the penalty differentials across offenses are tightly constrained for normative and institutional reasons, and offender impulsiveness is high, the Proportionality Rule fails to deter serious crimes and is not the optimal punishment rule. As an alternative, this paper proposes a Reduced Penalty Rule that imposes lighter sanctions on serious crimes and demonstrates that it can minimize social costs under specific conditions. This analysis provides theoretical guidance for policy design under law-enforcement resource constraints.