Optimal Warning Strategies: Punishment Ought Not to Be Inflicted Where the Penal Provision Is Not Properly Conveyed

Bentham (1789), Chapter 13, section iii.

Two exceptions are Emons (2007) and Rousseau (2009) which are discussed later in this section. For models dealing with optimal penalty schemes for repeat offenders see Chu et al. (2000), Emons (2003, 2004), Miceli and Bucci (2005), Mungan (2010, 2012), Polinsky and Shavell (1998), and Polinsky and Rubinfeld (1991). For a general review of the law and economics literature on law enforcement, see Garoupa (1997), Polinsky and Shavell (2000), and Polinsky and Shavell (2007).

Bentham (1789), Chapter 13, section iii.

Police officers may use discretion in issuing warnings. Section 4.5 contains a few comments regarding the use of discretion, but the theoretical part of this article abstracts from the issue and shows that hybrid warnings can be optimal even at the absence of discretion. For an economic analysis and discussion of the determination of optimal discretion, see Shavell (2007).

The relationship is weak because of corner solutions. More precisely, when the illegality of an act is unknown to a proportion of society exceeding a critical proportion (), it is optimal to use pure warnings (i.e. ). Accordingly, for proportions above this threshold, the optimal x is constant at 100. A similar result holds when the proportion of uninformed individuals is below a certain threshold (), in which case the optimal x is constant at 0. x is strictly increasing in the proportion of uninformed individuals () when . This result is discussed in further detail in Section 2, infra.

Warnings, in general, are meant to give notice to or caution individuals who are presumed to lack information regarding a certain issue. (See Black’s Law Dictionary’s (8th ed. 2004) definition of warning: ‘The pointing out of a danger, esp. to one who would not otherwise be aware of it.’)

Articles invoking the assumption that there are costs associated with such judicial errors include Stigler (1970), Posner (1973), Png (1986), Miceli (1990), Chu et al. (2000), and Lando (2009). See also Mungan (2011) and Rizzolli and Saraceno (2011), providing utilitarian justifications for the assumption that there are costs associated with the punishment of the innocent.

See, e.g. Folger and Konovsky (1989), Konovsky and Cropanzano (1991), and Tyler (1990), studying the negative effects of unfair procedures.

Sunshine and Tyler (2003:513), for instance, state that “the key antecedent of legitimacy is the fairness of the procedures used by the police”.

See, e.g. Tyler (1990:28): “A[n] approach to assessing legitimacy is to measure the extent to which authorities enjoy the public’s support, allegiance, and confidence (in political science often subsumed under the heading ‘trust in government’)”.

Seligson (1980).

See, e.g. Worchel et al. (1974).

Seligson (1980).

See, e.g. Wesbrook (1980).

Tyler (1990:58) finds that “[t]he results of the regressions suggest that legitimacy has a significant independent effect on compliance, even when other potential causal factors are controlled for”. See also Sunshine and Tyler (2003).

Tyler (1990:34-36) provides a list of studies examining the link between concepts related to legitimacy and socially costly behavior.

Sherman (1993:460).

On which, see Kaplow (1990).

Dana (2001) and Emons (2003) refer to the problem of punishing repeat offenders as a puzzle. This is because escalating punishments are observed frequently, but there are many models implying that this is a sub-optimal practice.

See note 2, supra.

See Harrington (1988), which deviates from the main framework for analyzing optimal punishments for repeat offenders. An implication of this article is that warnings may be optimal. However, this result is not due to the informational function of warnings, but due to the design of a mechanism which allows offenders to move from one group to another where the regulator determines the monitoring rates of each group. Accordingly, Harrington (1988) does not highlight the informational functions of warnings as the instant article does.

Furthermore, this conclusion requires that individuals must be constrained to choose between always committing a crime and never committing a crime, in other words, individuals’ strategies are constrained to be history independent.

Friehe (2009:167).

I assume that the government’s detection mechanism may generate the error of acquitting guilty individuals, but not the error of convicting innocent individuals. Incorporating such errors, which have been analyzed in the literature, e.g. by Rizzolli and Saraceno (2011) and Mungan (2011), may provide another justification for the use of warnings, because the cost of punishing an innocent individual presumably exceeds the cost of warning him. There is, however, an ongoing debate as to how such errors ought to be incorporated in crime and deterrence models (see, e.g. Garoupa and Rizzolli (2012) and Lando (2006)). I am, therefore, excluding such potential benefits from the social welfare calculus.

See Section 4.1., infra, for a discussion of how an endogenous p would interact with optimal warning strategies. See also Mungan (2010:174), arguing for the plausibility of this assumption: “This is a commonly employed assumption in the literature. Polinsky and Rubinfeld (1991), Burnovski and Safra (1994), Chu et al. (2000), Nyborg and Telle (2004), and Miceli and Bucci (2005) are examples of models which impose this assumption. Furthermore, when general enforcement is possible, for low levels of harm, p can be treated as a fixed value although it is endogenously determined. The last point is formalized in Shavell (1991) …”

A pure warning strategy refers to issuing warnings to all first-time offenders. The meaning of the word pure in this context is clearly distinguishable from its meaning in the context of pure strategies in game theory, where the word indicates that a player’s likelihood of playing a given strategy is 1. Stated differently, whereas in standard game theory the word pure refers to the likelihood of a given strategy being played, in the present context it refers to the proportion of individuals being warned.

Therefore, a person whose past crimes have gone unnoticed is considered a first-time offender.

When individuals are wealth constrained, as discussed in the literature (see, e.g. Polinsky and Shavell (2007)), it may be optimal to resort to non-monetary and therefore costly means of punishing individuals. The case of costly sanctions is briefly discussed in Section 4.2.

Robinson and Darley (2003, 2004) argue that many individuals do not know the exact content of the relevant criminal code. Some of these individuals may nevertheless not commit crime. It may appear that the instant model is at odds with this observation, since uninformed individuals are assumed to commit crime. This assumption is mainly simplifying, and one can consider a more realistic assumption which produces the same results as in this article. In particular, one may consider two types of uninformed individuals. The first commits crime whereas the second refrains from committing crime when uninformed. The latter type of individuals never commit crime and therefore need not be deterred or punished. Therefore, they have no impact on social welfare and can legitimately be left out of the social calculus. As such, one can proceed with the analysis as if the former and simpler assumption were true.

In Section 3, I demonstrate the purpose of having . This is mainly a simplifying assumption for expositional purposes and to ease the description of proofs. A weaker condition which would grant the same simplifying properties is . I also discuss the implications of having .

I assume that indifferent individuals do not commit crime.

This is true even for uninformed individuals whose actual net expected benefits are negative.

This proposition assumes . When , the optimal first period sanctions and warning strategies are such that .

See note 2, supra.

For the explicit expression for K and a brief explanation of the derivation of , see the proof of Proposition 3 in the Appendix.

This proposition reports results when . When any warning strategy accompanied by proper sanctions for first-time offenders is optimal. However, for expositional convenience, critical values and in Proposition 4 and Figure 3 are reported as functions with domain .

See note 19, supra.

See, e.g. Polinsky and Shavell (2007:413–414) showing that in the simple law enforcement model under-deterrence is optimal when p is endogenous, whereas it is not when p is exogenous.

See, e.g. Polinsky and Shavell (2007, sections 4–9).

See, e.g. Shavell (2007).

See note 2, supra.

See, e.g. Polinsky and Shavell (1984).

Consider, for instance, the following language, which is often used by the FBI to inform people of the consequences of copyright infringements: “The unauthorized reproduction or distribution of this copyrighted work is illegal. Criminal copyright infringement, including infringement without monetary gain, is investigated by the FBI and is punishable by up to 5 years in federal prison and a fine of $250,000.”

This is a direct implication of Proposition 4, which suggests that the optimal q is weakly decreasing in .

See Shavell (2007), for an extensive analysis as to when and how discretion should be allowed.

For instance by requiring police officers to issue warnings x% of the time and in a particular order.

See note 19, supra.

Emons (2003, 2004, 2007) are examples of such models.

See also Mungan (2012), reviewing the existing literature and pointing out that the assumption of fixed, rather than fluctuating, criminal tendencies may be responsible for the failure of many models to generate results that are consistent with our intuitions of justice.

It should be noted that is differentiable. To see this, evaluate both expressions for at and verify that they are equal using the definition for .