Why higher punishment may reduce deterrence

Rational juries that are uncertain about whether a defendant is actually guilty or not will minimize their expected preference costs from mistakenly convicting innocent defendants (Type I error) and from wrongly releasing guilty defendants (Type II error). In many cases, it seems plausible to assume that Type I errors become relatively more important for juries when punishments are high. If so, juries require a higher degree of certainty to cast a guilty vote when punishments are high, so that less defendants will be convicted. Deterrence is then decreasing for all punishments above a specific threshold as the direct effect of higher punishments will then be dominated by the indirect effect coming from a lower conviction probability. This has been pointed out by Andreoni (1991) but has not been taken up since then. We first confirm Andreoni's findings in our framework and then extend to the impact of legal quality, defined by the informativeness of evidence, on optimal fines. Our main result is that optimal fines tend to be increasing in legal quality. Since the seminal paper by Gary Becker (1968), economists have identified various reasons why legal systems do not impose maximum fines for all offenses. Stigler (1970) and Shavell (1992) point out that optimal fines increase in harm when criminals choose among several offenses as marginal deterrence becomes otherwise too small. Shavell (1991) shows that optimal fines are less than maximum when crimes are (partially) detected by general enforcement which, by definition, is suitable to detect a range of different offenses. When individuals are risk averse, Polinsky and Shavell (1979) argue that Draconian punishments would lead to an inefficient allocation of risk. Other papers focus on different kinds of ex post inefficiencies of high punishments, i.e. on inefficiencies arising after a crime has been committed. Malik (1990) emphasizes that high fines increase investments of criminals in reducing the risk of detection. And when punishments are socially costly as in the case of imprisonment, optimality requires that costs and deterrence are marginally balanced (Shavell, 1987). Besides the already mentioned paper by Andreoni (1991), Rubinfeld and Sappington (1987) also argue that social losses of wrong judgements depend on fines and focus on the incentives of defendants to invest in evidence provision. Among other results, they find that optimal fines are below social costs of convicting innocents under reasonable circumstances. Garoupa (2003) also mentions that costs of convicting innocents are increasing in punishments, but he does not perform a formal analysis of the impacts on deterrence. Finally, the legal literature on nullification pioneered by Michael and Wechsler (1937) argues that jurors or witnesses may refuse to participate in legal action when punishments seem unfairly high. This is related, but in our model, juries consider punishments as fair for guilty defendants, but are afraid of imposing high punishments on innocents. Section 2 presents the model. Section 3 analyzes the impact of punishments on deterrence, and Section 4 analyzes the impact of legal quality on the punishment that maximizes deterrence. Section 5 concludes.