Automated legal decision-making is often perceived as less fair than its human counterpart. This human-AI fairness gap poses practical challenges for implementing automated systems in the public sector. Drawing on experimental data from 4250 participants in three public decision-making scenarios, this study examines how different reasoning models influence the perceived fairness of automated and human decision-making. The results show that providing reasons enhances the perceived fairness of decision-making, regardless of whether decisions are made by humans or machines. Moreover, sufficiently individualized reasoning models have a stronger positive impact on the perceived fairness of automated decisions than on the perceived fairness of human decisions. This largely mitigates the human-AI fairness gap. The results thus suggest that well-designed reasons can improve the acceptability of automated governance.