Public law enforcement under ambiguity

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Highlights

  • Potential offenders have a vague idea of their own probability of being fined.

  • Potential offenders may either over or under estimate the probability of getting fined.

  • The standard Beckerian results may not hold, depending notably on the type of social welfare function.

  • It may be socially desirable to raise the means given to detection and to lower the fine accordingly.

Abstract

In real life situations, potential offenders may only have a vague idea of their own probability of getting caught and possibly, convicted. As they have beliefs regarding this probability, they may exhibit optimism or pessimism. Thus there exists a discrepancy between the objective expected fine and the subjective expected fine. In this context, we investigate how the fact that the choice whether or not to commit an harmful act is framed as a decision under ambiguity can modify the standard Beckerian results regarding the optimal fine and the optimal resources that should be invested in detection and conviction.

Introduction

In the public law enforcement framework à la Becker (1968), individuals are assumed to perfectly assess the probability of being fined if they commit an offense. However, in real life situations, potential offenders generally only have a vague idea of their own probability of getting caught and possibly, convicted. They have beliefs regarding the probability of detection and may exhibit optimism or pessimism. For instance, in the context of tax compliance, taxpayers tend to overestimate the probability of facing an investigation by the tax authority (Alm et al., 1992, Andreoni et al., 1998). In other situations, people are somewhat optimistic about their chances of not meeting with misfortune such as a car accident or illness (Jolls, 1998).

In our context, the way individuals estimate the probability of being detected will affect their decision whether or not to obey the law. This probability of detection and conviction is ambiguous while potential offenders know full well the amount of the sanction. The main justification for this hypothesis is that sanctions are often detailed in sentencing guidelines or penal codes, while information about the probability of detection cannot be given. Furthermore, uncertainty over the size of sanctions raises issues regarding the principle of equality before the law (Universal Declaration of Human Rights, 1948, article 7). Imagine Mr. A and Mr. B commit the same crime under the same circumstances. If Mr. A is sentenced to 5 years while Mr. B is sentenced to 3 years, the difference seems quite unfair.1

Most theoretical contributions based on the standard public law enforcement model (Polinsky and Shavell, 2007) assume that the probability of detection and conviction is known by potential offenders. The aim of our paper is to investigate how ambiguity regarding this probability can modify the classical results regarding the optimal fine and the resources a benevolent public law enforcer should invest in detection and conviction.2 Ambiguity, as defined by Snow (2010), is uncertainty about probability, created by missing information that is relevant and could be known. There exists several alternative models of choice under ambiguity (Etner et al., 2012). In this contribution, we adopt the Choquet expected utility framework and we represent the potential offender's beliefs on the probability of detection with a neoadditive capacity. Our framework is closed to Chateauneuf et al.'s (2007).

We consider successively two different objective functions for the authorities, denoted the populist and the paternalistic social welfare functions. These headings refer to Salanié and Treich (2009). They distinguish the populist regulator who “maximizes social welfare computed with citizens’ beliefs” from the paternalist regulator who “maximizes social welfare computed with the regulator's own belief”.3 Whether a regulator should adopt one approach or the other is subject to a debate in public economics (Pollak, 1998, Viscusi, 2000, Salanié and Treich, 2009, Johansson-Stenman, 2008).4 In particular, Johansson-Stenman (2008) supports that the regulator should take into account the discrepancy between the perceived and the objective risk as “the perceived risk affects individual utility directly”. This argument is in favor of the “populist” social welfare function. The author also refers to Becker and Rubinstein (2004) analysis of terror, where fear is inserted in the utility function. On the contrary, one reason to favor the paternalist approach is that the law enforcer may not observe these costs (such as the dis-utility of fear), or that what matters for society is what citizens are actually paying and not what they subjectively expect to pay.

In our public law enforcement setting, we look at the two social welfare functions (populist and paternalist), and we derive, in each case, the optimal enforcement policy.5 The key difference between the two approaches is whether the discrepancy between the objective and the perceived probability of fine should be taken into account by the law enforcer. Indeed, this discrepancy might generate a perception bias cost (gain) when individuals are pessimistic (optimistic). A paternalistic public law enforcer does not take into account the discrepancy between the expected and the actual expected fine, while the populist law enforcer does.

Our results call for the degree of pessimism of potential offenders in determining deterrence policy to be taken into account. Indeed, recommendations on deterrence policy can be widely affected by beliefs. Assume that individuals are pessimistic: they overestimate the probability of detection and conviction. We find that optimal fines may be lower for two reasons. First, fines may be considered as costly transfers if society takes mental suffering into account. Second, the subjective probability of detection is higher than the objective probability. Regarding the optimal means to invest in detection, our results go in different directions depending on the objective function of the law enforcer. When the law enforcer is populist (he/she takes into account the perception cost), we show that it may be socially desirable to raise the probability and to lower the magnitude of fine accordingly (in order to keep the deterrence level constant) if the marginal cost of detection is sufficiently small. In such a case, the fine is not necessarily maximal. When the law enforcer is paternalistic (he/she ignores the perception cost), the optimal fine is always maximal (as fines are costless transfers). And it is possible that the means invested in detection are lower than those in the absence of ambiguity only under certain conditions. In such a case, the objective probability of detection appears to be a less efficient deterrence tool due to the weight of the beliefs.

The remainder of the paper is organized as follows. Section 2 presents the related literature. In Section 3, we present the model of public enforcement of law under ambiguity. In Section 4, we study the optimal fine. In Section 5, both the monetary sanction and the probability of detection and conviction are endogenous. Section 6 concludes.

Section snippets

Related literature

To our knowledge, a limited number of papers have addressed the link between crime deterrence and ambiguity.6 Let us point out the most relevant contributions for our analysis.

Harel and Segal (1999) describe how the legal system actually favors certainty relative to the sanction (for instance, through specifying the

Assumptions and notations

Our framework elaborates on the conventional model of public law enforcement (Polinsky and Shavell, 2007). Risk-neutral individuals choose whether or not to commit an act that yields a private benefit b and generates an external harm per act D. The public law enforcer does not observe any type b but knows their distribution described by a general density function f(b) with support [0,B] and a cumulative distribution function F(b), with D<B. The proportion of offenders is equal to 1F(b˜), with b

The optimal deterrence policy when resources devoted to detection are given

In this section, we consider that enforcement expenditures are exogenous, resulting in a given probability of detection and conviction. In the absence of ambiguity surrounding the probability of detection and conviction, we know that the optimal fine equals sn*=min{Dp,w} and that the first-best outcome can be achieved as long as Dpw (see Appendix A for the proof).

Assume now that there is some ambiguity surrounding the probability of being fined. Section 4.1 exposes the results regarding the

The optimal deterrence policy when resources devoted to detection are endogenous

In this section, the public law enforcer determines both the size of the fine and the probability of detection. In the absence of ambiguity, we know since Becker's seminal model that the optimal fine should be maximal sn*=w (see Appendix A for the proof). In the remaining of the section, we assume that there is some ambiguity surrounding the probability of being fined, and we consider successively two cases, depending on whether the social welfare function includes the perception costs.

Conclusion

The aim of this paper is to provide some insights into how the degree of pessimism influences the socially optimal amount of fines and enforcement expenditures when potential offenders are unable to perfectly estimate the probability of detection and conviction. Two alternatives social welfare functions are considered. The populist social welfare function is computed with citizens’ perceived probability of sanction, while the paternalistic one is computed with the objective probability.

By

Authors’ contribution

Bertrand Chopard and Marie Obidzinski: conceptualization, formal analysis, writing – original draft, writing – review & editing.

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  • We are very grateful for their comments and suggestions to the participants at the “Behavioral Economics” seminar at Economix CNRS and Paris Nanterre University, and the 3rd French Law and Economics Annual Conference, and the American Law and Economics Association's annual conference (2019), and the Montpellier Research in Economics seminar, and the CRED seminar in Paris II. We are especially indebted to Alvaro Bustos, Johana Etner, Luigi Franzoni, Meglena Jeleva, Nuno Garoupa, Etienne Lehmann, Barbara Luppi, Lisa Morhaim, Mitchell Polinsky, Jennifer Reinganum for their fruitful suggestions. Any remaining errors or omissions are, of course, our own.

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