Fine reductions for self-reported offenses entail a potential trade-off. On the one hand, inducing offenders to self-report allows the social planner to save on enforcement costs and reduce harm through early detection. On the other hand, fine reductions may also reduce deterrence: offenders anticipate that if their detection probability turns out to be higher than initially expected, they can exploit the possibility of a more lenient sanction. We analyze how this trade-off is affected by the potential offender’s utility function, contrasting standard neoclassical preferences with loss aversion. For loss aversion, we apply the approach by Koszegi and Rabin (2006, 2007), in which reference points are determined by the ex ante expectations of equilibrium strategies. Assuming that the private benefit from crime is lost in case of detection, we distinguish between loss aversion in the fine dimension and in the benefit dimension. Intuitively, one might assume that loss aversion facilitates law enforcement because losses loom larger than gains, which sets incentives to refrain from crime. We show that a sufficient condition for this intuition to hold is that the degree of loss aversion in the fine dimension is weakly above the degree in the benefit dimension.

对自我报告的犯罪行为进行罚款减少需要一个潜在的权衡。一方面，诱导犯罪者自我报告可以让社会规划者节省执法成本并通过早期发现减少伤害。另一方面，罚款减少也可能降低威慑力：犯罪者预计，如果他们的发现概率高于最初的预期，他们可以利用更宽松的制裁的可能性。我们分析了这种权衡如何受到潜在犯罪者的效用函数的影响，将标准的新古典偏好与损失厌恶进行对比。对于损失厌恶，我们采用 Koszegi 和 Rabin (2006, 2007) 的方法，其中参考点由均衡策略的事前预期确定。假设一旦被发现，犯罪的私人利益就会丧失，我们区分了精细维度和收益维度的损失厌恶。直觉上，人们可能会假设损失厌恶有助于执法，因为损失比收益更大，这会激励人们避免犯罪。我们证明了这种直觉成立的充分条件是精细维度中的损失厌恶程度弱于收益维度中的程度。