BETTER THAT TEN INNOCENT PERSONS SUFFER THAN THAT ONE GUILTY SCAPE

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1 BETTER THAT TEN INNOCENT PERSONS SUFFER THAN THAT ONE GUILTY SCAPE Standards of evidence for pre-trial detentions GABRIEL DOMÉNECH University of Valencia Law School MIGUEL PUCHADES University of Valencia Law School Abstract: In most legal systems, a very high standard of evidence is established to reach a verdict of guilty. Accused individuals may not be convicted unless the prosecution proves their guilt beyond reasonable doubt. This contrasts with the much lower standards of evidence required to take pre-trial measures, even when these deprive some persons of their liberty. A mere reasonable suspicion of having committed a criminal offence is usually sufficient to lawfully detain a person with the aim of investigating the crime or preventing the risk of this individual avoiding prosecution or punishment, destroying evidence, influencing witnesses or committing any aitional offence. What is more, sometimes it is permissible to detain persons even without any such individualized suspicion at all. The present paper shows why standards for detentions should be lower than that for conviction: wrongful non-detentions have a more negative impact on deterrence than wrongful detentions. The paper also analyzes how those standards should vary depending on certain circumstances, and suggests that the model and the results presented can be extended to other preliminary measures taken in the criminal procedure. Keywords: criminal procedure, pre-trial detention, seizures, judicial errors, optimal standard of evidence JEL Classification: K14, K42 I. INTRODUCTION The title of this paper obviously constitutes a paraphrase of the famous Blackstonian sentence, it is better that ten guilty persons escape than that one innocent suffer 1. The idea formulated in this assertion, and by many other authors in different ways throughout history 2, is a cornerstone of criminal law in modern societies. Criminal Courts inevitably make mistakes. They sometimes convict accused individuals who really did not commit the crimes charged, while other times they acquit defendants who were actually guilty. The Blakstone s formulation expresses that the former (type I) errors are worse than the latter (type II) ones. Courts should therefore try to especially avoid wrongful convictions, rather than wrongful acquittals. Criminal law should hence be designed in a biased way, in favor of defendants 3. The most important manifestation of such asymmetric design is the requirement of a high standard of evidence in order to reach a verdict of guilty. This so called principle of in dubio pro reo is well established in contemporary criminal systems. Under the case law of the Supreme Court of the United States, for instance, defendants See BLACKSTONE (1769), at p See VOLOKH (1997). See HYLTON and KAHNNA (2007).

2 may not be convicted unless their guilt is proved beyond a reasonable doubt 4. Similarly, the European Court of Human Rights has declared that the principle of the presumption of innocence requires that any doubt should benefit the accused 5 ; it is a basic requirement of criminal justice [that] the prosecution has to prove its case beyond reasonable doubt ; the in dubio pro reo is one of the fundamental principles of criminal law embeed in the right to a fair trial under Article 6 1 of the Convention 6. This strict standard sharply contrasts with that usually required in civil cases (e. g. preponderance of the evidence ), according to which the plaintiff prevails if she manages to prove that her allegations are more likely to be true than not true 7. It should be pointed out, however, that the principle of in dubio pro reo is far from being universally applied even in criminal cases. On the contrary, it is only to be used in the very final stage of the criminal procedure, when the competent court or jury has to assess the defendant s guilt in order to either convict or acquit her. Before then, the general rule could well seem the opposite: in dubio contra civem. A lower standard of evidence is indeed required when public agents take measures aimed at investigating crimes or preventing the risk of suspects fleeing and avoiding prosecution or punishment, destroying evidence, influencing witnesses or committing any aitional offence. Even when these pre-trial measures imply the deprivation of the liberty of the affected individuals, it is not necessary for the prosecution to prove that they are guilty beyond any reasonable doubt. Under article 5 1(c) of the European Convention of Human Rights, for example, a mere reasonable suspicion of having committed an offence is needed to lawfully arrest or detain a person for the purpose of bringing him before the competent legal authority. As the European Court has declared, facts which raise a suspicion need not be of the same level as those necessary to justify a conviction or even the bringing of a charge, which comes at the next stage of the process of criminal investigation 8 ; it is only required that the elements of which the authorities have knowledge at the time when the order is issued are reasonably sufficient to believe that the detainee has committed an offence 9. Under the fourth amendment of the U.S. Constitution, [the] right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized. The U.S. Supreme Court early observed that the term probable cause, according to its usual acceptation, means less than evidence which would justify condemnation It imports a seizure made under circumstances which warrant suspicion In re Winship, 397 U.S. 358 (1970). Judgment of the ECHR of 6 December 1988 (Barberà, Messegué and Jabardo v. Spain, 10590/83, 77). Judgment of the ECHR of 13 December 2011 (Adjarić v. Croatia, 20883/09, 51). See, for instance, BROOKS (1982). For an economic analysis of this standard, LANDO (2002). Judgment of the ECHR of 28 October 1994 (Murray v. the United Kingdom, 14310/88). Judgment of the ECHR of 11 January 2001 (N.C. v. Italy, 24952/94). Locke v. United States, 7 Cranch 11 U.S. 339, 348 (1813)]. See also Bell v. Wolfish, 441 U.S. 520, 533 (1979). [2]

3 The wording of these and other legal opinions suggests that the amount of supporting evidence required to take such pre-trial measures could be even lower than that needed under the preponderance of evidence standard. It seems that, when deciding on those measures, type II errors are worse than type I ones: it is better than one innocent person or eventually hundreds of them suffer than that one guilty escape 11. This paper tries to analyze whether and why this intriguing result is justified from an economic point of view. It proceeds as follows. Section II presents the basic model. Section III shows why the standard of evidence required to convict accused individuals is so high ( beyond any reasonable doubt ). As RIZZOLLI and SARACENO (2011) have demonstrated, costs of punishment can well explain the high standard of evidence required to reach a verdict of conviction. The rationale is that there is an asymmetry between the costs of wrongful conviction and wrongful acquittal. Both types of errors have the same negative impact on deterrence, but the former are more costly because of the direct costs of punishment. Section IV shows why the standards of evidence established to take pre-trial measures restricting individuals rights could be lower (e. g. reasonable suspicion ). When deciding on whether or not to detain suspects of having committed criminal offences, type II errors have a more intense impact on deterrence than type I ones. The explanation is quite simple. When detained, individuals bear two types of costs: those already derived from detention and the expected costs of being eventually convicted. The former are the same for both guilty and innocent detainees. The latter, on the contrary, are higher for guilty individuals, insofar as their probability of being convicted after the trial is higher as well. Section V analyzes how the standards for detentions should vary depending on some circumstances. Section VI shows that our results are consistent with current law. Section VII suggests some possible extensions and section VIII concludes. II. BASIC MODEL Let us assume that individuals choose between committing an offence and obeying the law by comparing the private benefits and costs they expect to derive from crime Private gains from crime Offenders derive some benefits from engaging in illegal activities. Let ww jj be the private gain individual jj obtains from committing a crime. It must be noted that ww jj is an assessment of subjective nature, which varies across individuals as a result of the existing differences between them in preferences, moral constraints, reputation concerns, risk aversion, opportunity costs of criminal activity, etc. A significant share of the population would thus probably experience low utility from committing crime while some individuals place a higher value on it. Let us assume that ww is distributed according to a probability density distribution zz(ww) and a cumulative distribution function ZZ(ww). Hence, ZZ(ww 0 ) indicates the share of the population that would obtain The U.S. Supreme Court has held permissible detention programs with success rates of 1.5% [Michigan Department of State Police v. Sitz, 496 U.S. 444, 455 (1990)] and even 0.12% [United States v. Martinez-Fuerte, 428 U.S. 543, 554 (1976)]. BECKER (1968), at p [3]

4 gains from crime that are lower than ww 0, while 1 ZZ(ww 0 ) denotes the share of the population that would derive benefits from it higher than ww Expected private costs from detention and conviction The population can be classified into different subsets made up of criminals and law-abiding individuals. Public agents investigate only one of these subsets. Both criminals and law-abiding citizens face therefore a probability of being investigated as suspects of having committed an offence. Let us denote pp gg as the probability of guilty persons being investigated for that reason and pp ii the probability of innocent ones being the target of such an investigation. It is realistic to assume that pp gg > pp ii. Before trial, there is certain net incriminating evidence ee against individuals who are being investigated. The collection of this evidence is a costless activity, and its amount only depends on whether or not they committed the offence. We consider hence ee as an exogenous random variable distributed according to two probability density distributions conditional on whether suspects being guilty or innocent. Let us denote gg pp (ee ) as the density function of incriminating evidence ee for guilty persons, and ii pp (ee ) the density function of incriminating evidence for innocent ones. GG pp (ee ) and II pp (ee ) are the corresponding cumulative distribution functions for guilty and innocent individuals respectively. We may reasonably assume that II pp (ee ) > GG pp (ee ) ee > 0, which implies that the amount of incriminating evidence existing against factually guilty individuals before the trial is, on average, larger than the amount against innocent ones. Investigated individuals are detained if such net incriminating evidence ee exceeds certain legal standard ee. Otherwise, they are not. The probability of a factually guilty person suffering investigation and detention is therefore pp gg 1 GG pp (ee ), and that of an innocent one pp ii 1 II pp (ee ). We define the term detention in a very broad sense, as every kind of deprivation or restriction of individual liberty carried out by state agents before trial, no matter for how long, in order to enforce criminal law. So defined, detentions can range from brief stops lasting a few seconds to pre-trial detentions for some years, through formal arrests extending over several days. Detention entails costs for both the detainees, cc, and the society, cc. The former arise from: loss of liberty, income, reputation and self-esteem; emotional distress; demoralization effects of being publicly humiliated or placed in alien surroundings; risk of being abused or attacked by other inmates; cut off from friends and family; dislocation costs in adjusting back to life in the outside, etc. 13 The latter include, for instance, negative psychological, stigmatizing and monetary impacts on family members of detainees 14, and financial costs incurred by the State in order to fund the detention system. We also define the term trial in a very broad, non technical sense, as the process carried out in order to determine the detainee s innocence or guilt, and correspondingly either to acquit or to punish him. It must be noticed that, in this sense, every detainee is tried, ant that some trials take place not before a Court but a police officer See MANNS (2005), at pp et seq.; SCHROEDER (1993), at pp See MANNS (2005), at pp and [4]

5 During the trial, a certain amount of net incriminating evidence ee cccccccc is collected against the defendant. This amount could well depend on several factors such as the personal abilities of the defense attorney and the prosecutor, the resources invested by them in the production of evidence, etc. Let us suppose, nevertheless, that such production is a costless activity and that ee cccccccc only depends on whether or not the defendant committed the offence as charged. We also model ee cccccccc as an exogenous random variable distributed according to two probability density functions conditional on whether the defendant being guilty or innocent. Let gg tt (ee cccccccc ) the probability density function of incriminating evidence ee cccccccc for guilty defendants, and ii tt (ee cccccccc ) the density function of incriminating evidence ee cccccccc for innocent ones. The corresponding cumulative distribution functions are denoted as GG tt (ee cccccccc ) and II tt (ee cccccccc ) respectively. We also suppose that II tt (ee cccccccc ) > GG tt (ee cccccccc ) ee cccccccc > 0, which implies that the amount of incriminating evidence generated against a factually guilty defendant is, on average, larger than the amount collected against an innocent one. It must be underlined that ee and ee cccccccc are not the same variables, nor gg pp (ee ) and ii pp (ee ) are the same functions as gg tt (ee cccccccc ) and ii tt (ee cccccccc ) respectively, although they could be related. The same applies to GG pp (ee ), II pp (ee ), GG tt (ee cccccccc ), and II tt (ee cccccccc ). Once the trial has concluded, accused persons are convicted and punished only if incriminating evidence exceeds certain standard ee cccccccc. Otherwise, they are acquitted. Given a standard ee cccccccc, the probability of a guilty defendant being convicted is 1 GG tt (ee cccccccc), and that of an innocent one is [1 II tt (ee cccccccc)]. The probability of a guilty individual being investigated, detained and convicted is therefore pp gg 1 GG pp (ee )[1 GG tt (ee cccccccc)], and that of her or him being investigated, detained and acquitted is pp gg 1 GG pp (ee )GG tt (ee cccccccc). Likewise, the probability of an innocent individual being investigated, detained and convicted is pp ii 1 II pp (ee )[1 II tt (ee cccccccc)], and that of her or him being investigated, detained and acquitted is pp ii 1 II pp (ee )II tt (ee cccccccc). Punishment implies costs for the convicted cc pppp as well as for the rest of society cc pppp. These costs are similar in nature to those aforementioned of pre-trial detention, albeit much higher: cc cc pppp and cc cc pppp. On the one hand, because detention, if lawfully imposed, may not last longer than the imprisonment detainees can suffer if they are finally convicted and, on the other hand, because conviction has arguably more intense stigmatizing effects than detention. Let us suppose that if defendants are sentenced to imprisonment, the period spent on remand is deducted from prison time. 3. Decision to commit crime Individuals, who are supposed to be rational and risk neutral, will commit a crime if the expected private gains from infringing the law exceed the private costs of obeying it. The critical threshold from which those gains become superior to these costs can be denoted as ww. Let us remember that ww is distributed according to a probability distribution zz(ww) and a cumulative distribution ZZ(ww). By normalizing population to 1, the probability of an individual engaging in criminal activity is then 1 ZZ(ww). This also corresponds to the crime rate for the entire population. [5]

6 Individuals choose to commit crime if their expected net payoff from infringing the law exceeds their net payoff from obeying it, i.e. if: ww jj pp gg 1 GG pp (ee )GG tt (ee cccccccc)cc pp gg 1 GG pp (ee )[1 GG tt (ee cccccccc)]cc pppp > pp ii 1 II pp (ee )II tt (ee cccccccc)cc pp ii 1 II pp (ee )[1 II tt (ee cccccccc)]cc pppp [1] That is, individuals engage in crime if ww jj > ww where ww = pp gg 1 GG pp (ee )GG tt (ee cccccccc) pp ii 1 II pp (ee )II tt (ee cccccccc)cc + pp gg 1 GG pp (ee )[1 GG tt (ee cccccccc)] pp ii 1 II pp (ee )[1 II tt (ee cccccccc)]cc pppp [2] III. OPTIMAL STANDARDS OF EVIDENCE FOR CONVICTION 1. Standard for conviction that maximizes deterrence Let us denote, for simplicity reasons, OO(ee, ee cccccccc) as the crime rate for the entire population. That is: OO(ee, ee cccccccc) = 1 ZZ(ww) First order condition to minimize crime rate (i. e. maximize deterrence) with respect to the standard for conviction is: (ee,ee cccccccc ) cccccccc zz(ww) pp ii1 II pp (ee )ii tt (ee cccccccc ) pp gg 1 GG pp (ee )gg tt (ee cccccccc ) cc pppp cc = 0 [3] That is: pp ii 1 II pp (ee )ii tt (ee cccccccc ) = pp gg 1 GG pp (ee )gg tt (ee cccccccc ) [4] We can assume that there is at least one standard of evidence for conviction ee cccccccc that allows public agents to distinguish between innocent and guilty individuals more accurately after the trial (when deciding on their conviction) than before (when deciding on their detention). If it were not the case, the trial would be entirely pointless. Consequently, we assume that there is at least one standard of evidence ee cccccccc such that ii tt (ee cccccccc ) > pp gg1 GG pp (ee ) [5] gg tt (ee cccccccc ) pp ii 1 II pp (ee ) Given that, as GG tt (ee cccccccc ) and II tt (ee cccccccc ) are continuous and differentiable over the interval (0, ), and GG(ee) II(ee) ee, there exists a standard of incriminating evidence for conviction ee cccccccc which maximizes deterrence such that the marginal probability of a [6]

7 guilty individual being acquitted equals the marginal probability of an innocent one being acquitted: pp ii 1 II pp (ee )ii tt (ee cccccccc ) = pp gg 1 GG pp (ee )gg tt (ee cccccccc ) [6] As pp gg 1 GG pp (ee ) > pp ii 1 II pp (ee ), the standard of conviction that maximizes deterrence is such that ii tt (ee cccccccc ) > gg tt (ee cccccccc ) [7] Proof: We assume that there is at least one ee cccccccc 0 such that pp ii 1 II pp (ee )ii tt (ee cccccccc ) > pp gg 1 GG pp (ee )gg tt (ee cccccccc ). As GG tt (ee cccccccc ) is a cumulative distribution, which implies that lim GG tt(ee cccccccc ) = 1, then there must be an ee ccoooooo2, very close to, such eeeeeeeeee that GG tt (ee cccccccc2 ) = 1. As II tt (ee cccccccc ) is a cumulative distribution as well, which implies that lim II tt(ee cccccccc ) = 1, and GG tt (ee cccccccc ) II tt (ee cccccccc ) ee cccccccc, then there must exist an eeeeeeeeee ee cccccccc1 < ee ccccccvv2 such that II tt (ee cccccccc1 ) = 1. Then, ii tt (ee cccccccc ) gg tt (ee cccccccc ) at least for ee cccccccc [ee cccccccc1, ee cccccccc2 ]. As pp ii 1 II pp (ee ) < pp gg 1 GG pp (ee ), then pp ii 1 II pp (ee )ii tt (ee cccccccc ) < pp gg 1 GG pp (ee )gg tt (ee cccccccc ) at least for ee cccccccc [ee cccccccc1, ee cccccccc2 ] as well. Consequently, as GG tt (ee cccccccc ) and II tt (ee cccccccc ) are continuous and differentiable over (0, ), then there must also exist at least one ee cccccccc 0 for which pp ii 1 II pp (ee )ii tt (ee cccccccc ) = pp gg 1 GG pp (ee )gg tt (ee cccccccc ). One can see that the negative impact of type I errors (wrongful convictions) on deterrence is exactly the same as that of type II ones (wrongful acquittals) 15. The crime rate increases equally with equal increases in the probabilities of both types of mistakes: OO(ee,ee cccccccc ) = OO(ee,ee cccccccc ) = zz(ww)cc pp gg 1 GG pp (ee )GG tt (ee cccccccc) pp ii 1 II pp (ee )[1 II tt (ee cccccccc)] pppp cc > 0 [8] 2. Standard for conviction that minimizes social costs As RIZZOLLI and SARACENO (2011) have shown, punishment costs can explain the high standard of evidence required to reach a verdict of guilty. The rationale is that there is an asymmetry between the costs of wrongful conviction and wrongful acquittal. Both types of errors have the same negative impact on deterrence 16, but the former are socially costlier because of the costs of punishment. Let see it. Criminal offences directly cause harm HH to society. Let us suppose that such harm is always higher than the private gains ww derived from infringing the law, HH > ww, and that hence crime always implies a direct, net social cost h = HH ww. Let us also assume In the law and economics literature this result was first pointed out by PNG (1986). Nonetheless, RIZZOLLI and STANCA (2012) have also shown that, if individuals are risk averse, wrongful convictions have a stronger negative impact on deterrence than wrongful acquittals. [7]

8 that total net harm crime directly causes on society is proportional to the number of offences committed. For simplicity reasons, we normalize population to 1, so the number of offenders equals the crime rate OO(ee, ee cccccccc) and the number of innocent individuals is 1 OO(ee, ee cccccccc). Besides the harm directly resulting from offences, crime makes necessary to incur the costs of enforcing the law, that is of pre-trial detention CC DD = cc + cc and punishment CC PP = cc pppp + cc pppp. Let us denote TC as the sum of all the social costs caused by crime and prevention of crime, which include: Direct costs of crime OO(ee, ee cccccccc)h Costs of detention pp gg 1 GG pp (ee )OO(ee, ee cccccccc) + pp ii 1 II pp (ee )[1 OO(ee, ee cccccccc)]cc DD Costs of conviction pp gg 1 GG pp (ee )OO(ee, ee cccccccc)[1 GG tt (ee cccccccc)] + pp ii 1 II pp (ee )1 OOee cccccccc, ee cccccccc[1 II tt (ee cccccccc)](cc PP CC DD ) Therefore, total social cost derived from crime can be represented as follows: TTTT = OO(ee, ee cccccccc)h + pp gg1 GG pp (ee )OO(ee, ee cccccccc) + pp ii 1 II pp (ee )[1 OO(ee, ee cccccccc)] CC DD + pp gg1 GG pp (ee )[1 GG tt (ee cccccccc)]oo(ee, ee cccccccc) + pp ii 1 II pp (ee )[1 II tt (ee cccccccc)][1 OO(ee, ee cccccccc)] (CC PP CC DD ) [9] The standard of incriminating evidence for conviction that minimizes social cost is the one such that ee cccccccc = OO (ee cccccccc )h + OO (ee cccccccc ) pp gg1 GG pp (ee ) ee cccccccc pp ii 1 II pp (ee ) CC DD + OO (ee cccccccc ) pp gg1 GG pp (ee )[1 GG tt (ee cccccccc )] pp ii 1 II pp (ee )[1 II tt (ee cccccccc )] + pp ii 1 II pp (ee )ii tt (ee cccccccc ) OO(ee cccccccc ) pp gg 1 GG pp (ee )gg tt (ee cccccccc ) (CC PP CC DD ) = 0 [10] pp ii 1 II pp (ee )ii tt (ee cccccccc ) It must be noticed that the standard of evidence for conviction which maximizes deterrence ee cccccccc does not satisfy this equation. Indeed, given that standard, then [8]

9 OO (ee cccccccc) = 0 as well as pp ii 1 II pp (ee )ii tt (ee cccccccc) pp gg 1 GG pp (ee )gg tt (ee cccccccc) = 0, so in such a case cccccccc pp ii 1 II pp (ee )ii tt (ee cccccccc)(cc PP CC DD ) < 0 [11] The sign of [11] follows directly from the assumptions that II tt (ee cccccccc ) is a continuous increasing function, so ii tt (ee cccccccc) > 0, and that CC PP > CC DD. It means that total cost is still decreasing at the point where the standard of evidence for conviction minimizes crime rate. Consequently, TC can still be reduced if a standard higher than ee cccccccc is established. Raising the standard of conviction from 0 up to ee cccccccc obviously reduces total social cost; as the volume of criminal activity decreases, both direct costs of crime and costs of detention and punishment diminish. Above ee cccccccc, costs of punishment continue to converge to zero but social harm resulting from the rise of crime rate and costs of detention start to rise at an increasing rate, which will finally lead to an increase of the total social costs. In conclusion, there exists a standard of evidence for conviction that minimizes social costs ee cccccccc which is higher than the standard for conviction that maximizes crime deterrence, ee cccccccc > ee cccccccc. IV. OPTIMAL STANDARDS OF EVIDENCE FOR DETENTION 1. Standard for detention that maximizes deterrence First order condition to minimize the crime rate with respect to the standard for detention is: OO(ee,ee cccccccc ) = pp ii ii pp (ee ) pp gg gg pp (ee )cc pppp + zz(ww) = 0 [11] pp gg gg pp (ee )GG tt (ee cccccccc) pp ii ii pp (ee )II tt (ee cccccccc)cc pppp cc Therefore, the standard for detention that maximizes deterrence ee is such that pp ii ii pp (ee )[1 II tt (ee cccccccc)]cc pppp + II tt (ee cccccccc)cc = pp gg gg pp (ee )[1 GG tt (ee cccccccc)]cc pppp + GG tt (ee cccccccc)cc [12] Deterrence is thus maximized when the standard for detention ee is such that the marginal probability of innocent individuals being detained times the expected costs incurred by them as a consequence of their detention equals the marginal probability of guilty individuals being detained times the expected costs that detention implies for them. Furthermore, given that: [9]

10 II tt (ee cccccccc) > GG tt (ee cccccccc), pp ii < pp gg, [1 II tt (ee cccccccc)]cc pppp + II tt (ee cccccccc)cc > 0, and that [1 GG tt (ee cccccccc)]cc pppp + GG tt (ee cccccccc)cc > 0, then we can conclude that ii pp (ee ) > gg pp (ee ) If equation [12] holds, second order condition to minimize the crime rate is met where the standard for detention is such that pp ii ii pp(ee )[1 II tt (ee cccccccc)]cc pppp + II tt (ee cccccccc)cc < pp gg gg pp (ee )[1 GG tt (ee cccccccc)]cc pppp + GG tt (ee cccccccc)cc [13] This condition is obviously fulfilled when ii pp (ee ) < 0 and gg pp (ee ) > 0, that is, when ii pp (ee ) decreases while gg pp (ee ) increases in ee. If equation [12] never holds, whatever the standard of detention, there is a corner solution. The standard of detention that maximizes deterrence is then zero. Every investigated individual should be detained as well. There exists such a corner solution if and only if: OO(ee,ee cccccccc ) > 0 ee > 0 That is, if: pp ii ii pp (ee )[1 II tt (ee cccccccc)]cc pppp + II tt (ee cccccccc)cc < pp gg gg pp (ee )[1 GG tt (ee cccccccc)]cc pppp + GG tt (ee cccccccc)cc ee > 0 [14] Given that II tt (ee cccccccc) > GG tt (ee cccccccc) ee and that there is a range of values for ee such that ii pp (ee ) > gg pp (ee ), condition [14] is more likely to be met: the lower the ratio between the probabilities of being investigated for innocent an guilty individuals pp ii is; the lower the private costs of detention are; the higher the private costs of pp gg conviction are; the more accurate the trial in distinguishing innocent individuals from guilty ones [that is, the greater is II tt (ee cccccccc) GG tt (ee cccccccc)] is; and the lower the maximal difference between the marginal probability of detaining the former [ii pp (ee )] and the marginal probability of doing the same with the latter [gg pp (ee )] is. In any case, the standard of detention that maximizes deterrence is such that the marginal probability of an innocent being detained is way higher than that of a guilty [10]

11 individual being detained [that is, ii pp (ee ) > gg pp (ee )]. The explanation is quite simple. When detained, individuals bear two types of costs: those already derived from detention and the expected costs of being eventually convicted. The former are the same for both guilty and innocent detainees. The latter, on the contrary, are higher for guilty individuals, as their probability of being convicted after the trial is also higher, 1 II tt (ee cccccccc) < 1 GG tt (ee cccccccc). Wrongful non-detentions have consequently a more negative impact on deterrence than wrongful detentions. Crime rate increases more with an increase in the probability of former mistakes being committed than with an equal increase in the probability of latter ones. OO(ee,ee cccccccc ) pp gg GG pp (ee ) = zz(ww)[1 GG tt(ee cccccccc)]cc pppp + GG tt (ee cccccccc)cc [15] OO(ee,ee cccccccc ) pp ii [1 II pp (ee )] = zz(ww)[1 II tt(ee cccccccc)]cc pppp + II tt (ee cccccccc)cc [16] As GG tt (ee cccccccc) < II tt (ee cccccccc), then OO(ee,ee cccccccc ) pp gg GG pp (ee ) > OO(ee,ee cccccccc ) pp ii [1 II pp (ee )] [17] Type I errors certainly reduce the benefits of obeying the law {[1 II tt (ee cccccccc)]cc pppp + II tt (ee cccccccc)cc being the reduction for each mistake}, but not so much as type II errors increase the benefits of committing crime {[1 GG tt (ee cccccccc)]cc pppp + GG tt (ee cccccccc)cc being the marginal increase}. If public agents want to maximize deterrence, they should therefore try to specially avoid letting guilty individuals to escape, rather than to prevent innocent ones from suffering detention. 2. Standard for detention that minimizes social costs First order condition of the standard of incriminating evidence for detention that minimizes social costs ee is such that = OO (ee pp gg gg pp (ee )OO(ee )h + OO (ee OO (ee II tt (ee cccccccc )] pp gg gg pp (ee ) pp gg 1 GG pp (ee ) pp gg 1 GG pp (ee ) pp ii 1 II pp (ee ), ee cccccccc ) pp ii ii pp (ee )[1 OO(ee, ee cccccccc )] CC DD + )[1 GG tt (ee cccccccc )] pp ii 1 II pp (ee )[1 )[1 GG tt (ee cccccccc )]OO(ee, ee cccccccc ) pp ii ii pp (ee )[1 II tt (ee cccccccc )][1 OO(ee, ee cccccccc )] (CC PP CC DD ) = 0 [18] One can see that if ee = ee, then [11]

12 < 0 [19] The sign of [19] is indeed negative as: OO (ee ) = 0, pp gg > pp ii, ii pp (ee ) > gg pp (ee ), and II tt (ee cccccccc ) > GG tt (ee cccccccc ). It means that the total social costs function is still decreasing at the point where the standard of evidence for detention minimizes crime rate. Total social costs can therefore be reduced if a standard higher than ee is established. We can consequently conclude that the standard for detention that minimizes social costs is higher than the standard for detention that minimizes crime rate: ee < ee [20] It must be pointed out that when the standard of detention is higher than that which maximizes deterrence then crime increases, and it does at an especially high rate. For instance, by comparing equations [3] and [11], one can see that when the standards of detention and conviction are such that ii pp (ee ) = gg pp (ee ) and ii tt (ee cccccccc) = gg pp (ee cccccccc) the impact on crime rate is greater for increases in the former standard than for increases in the latter, as one may reasonably assume that, after the trial, courts can distinguish between innocent and guilty individuals better than before it, that is, II tt (ee cccccccc) GG tt (ee cccccccc) > II pp (ee ) GG pp (ee ). The impact will be even greater if higher standards are established. This highly negative impact on crime caused by fixing the standard for detention above that which maximizes deterrence tends to cancel direct decreasing costs of detaining and convicting people, and pushes down the standard for detention that minimizes social costs, making it lower than that required for conviction. Furthermore, the standard of evidence for detention that minimizes social costs may be a corner solution, where every investigated individual is detained as well. This solution exists when the total social costs function is continuously growing [that is, > 0 ee > 0], which in turn requires that a double condition be met: On the one hand, crime rate must be continuously increasing with respect to the standard for detention: OO (ee ) > 0 ee > 0 [21] On the other hand, the harm caused directly by crime must be sufficiently high, namely [12]

13 h > pp gg gg pp (ee )OO(ee, ee cccccccc ) + pp ii ii pp (ee )[1 OO(ee, ee cccccccc )] + OO (ee ) pp gg gg pp (ee )OO(ee, ee cccccccc )[1 GG tt (ee cccccccc )] + pp ii ii pp (ee )[1 OO(ee, ee cccccccc )][1 II tt (ee cccccccc )] (CC PP CC DD ) + [II OO (ee ) pp(ee ) GG pp (ee )]CC DD + pp gg 1 GG pp (ee )[1 GG tt (ee cccccccc )] pp ii 1 II pp (ee )[1 II tt (ee cccccccc )](CC PP CC DD ) [22] CC DD As one can easily see, the higher h and OO (ee ) are, the more likely such a corner solution is. V. FACTORS INFLUENCING OPTIMAL STANDARDS OF EVIDENCE FOR DETENTIONS 1. Standard for detention that maximizes deterrence This standard will be lower (or, as previously noted, a corner solution minimizing crime rate will be more likely to exist) as: (1) private costs of detention cc decrease; (2) the number of acquitted actually innocent defendants II tt (ee cccccccc) increases; (3) the number of acquitted actually guilty defendants GG tt (ee cccccccc) decreases; (4) the probability of guilty individuals being investigated pp gg increases; (5) the probability of innocent individuals being investigated pp ii decreases; (6) the private costs of punishment cc pppp increase; (7) the standard for conviction ee cccccccc increases; and (8) acquitted detainees are compensated for the harm suffered as a consequence of detention. (1) If the direct private costs of detention (which are the same for both guilty and innocent detainees) decrease, the asymmetry between wrongful non-detentions and wrongful detentions becomes more acute, as the expected costs of being convicted (which are higher for guilty defendants than for innocent ones) intensify their positive impact on deterrence, thereby making detention more beneficial than before. Indeed, given that II tt (ee cccccccc) > GG tt (ee cccccccc), ii pp (ee ) > pp gg (ee ), and that public agents can distinguish between innocent and guilty individuals better after the trial than before the stage of investigation, then pp ii ii pp (ee )II tt (ee cccccccc) > pp gg gg pp (ee )GG tt (ee cccccccc). Therefore: cc OOee,ee cccccccc ee cc OOee,ee cccccccc ee <0 > 0 [23] >0 (2) If the number of innocent defendants who are finally acquitted increases (as a consequence, for instance, of an improvement in the evidence technology used in trial), then, ceteris paribus, the standard for conviction that minimizes crime rate will be lower: II tt (ee cccccccc ) OOee,ee cccccccc ee II tt (eecccccccc ) OOee,ee cccccccc ee >0 < 0 [24] >0 [13]

14 The result is also intuitive. As the number of wrongful convictions decreases, lowering the standard for detention in order to catch more criminals becomes less costly than before, insofar as less factually innocent individuals are punished. (3) Conversely, if the number of factually guilty detainees who are convicted increases, then the standard for conviction that minimizes crime rate will be higher: GG tt (ee cccccccc ) OOee,ee cccccccc ee GG tt (eecccccccc ) OOee,ee cccccccc ee <0 > 0 [25] >0 (4) If, ceteris paribus, the probability of factually guilty individuals being investigated increases (as a consequence, for instance, of a refinement of the criteria applied to determine the target population) then the standard for conviction that minimizes crime rate will be lower: pp gg OOee,ee cccccccc ee ppgg OOee,ee cccccccc ee >0 < 0 [26] >0 As more criminals enter now in the investigation pool, the marginal benefits of reducing the standard of detention in order to catch them are higher than before. (5) Conversely, if the probability of innocent individuals being investigated increases, then the standard for conviction that minimizes crime rate will be higher: pp ii OOee,ee cccccccc ee pp ii OOee,ee cccccccc ee <0 > 0 [27] >0 (6) If the private costs of punishment increase, deterrence is improved as this increase amplifies the asymmetry between the costs of wrongful non-detentions and wrongful detentions. Let us remember that the probability and, consequently, the expected costs of being punished are greater for guilty individuals than for innocent ones. After such an increase, the marginal deterrence benefits of reducing the standard for detention become greater. cc pppp OOee,ee cccccccc ee cc OOee,ee cccccccc ee >0 < 0 [28] >0 (7) If the standard for conviction is higher than the standard for conviction that maximizes deterrence, increases in the former standard will increase crime rate. As then there will be more criminals, the marginal benefits of reducing the standard of detention in order to catch them will augment. Indeed, one can see that [14]

15 cccccccc OOee,ee cccccccc ee cccccccc OOee,ee cccccccc ee >0 < 0 [29] >0 (8) Let us suppose that every acquitted individual is entitled to compensation for the harm suffered as a consequence of having been detained. Such compensation modifies the expected net payoff from committing crime or staying within the law. Now individuals choose to commit crime if ww jj > ww where ww = pp gg1 GG pp (ee )1 GG pp (ee ) pp ii 1 II pp (ee )[1 II tt (ee cccccccc)] cc pppp [30] By comparing expressions [30] and [2] one can see that compensating acquitted individuals deters crime if pp ii 1 II pp (ee )II tt (ee cccccccc) > pp gg 1 GG pp (ee )GG tt (ee cccccccc) [31] That is, if the probability of investigating, detaining and acquitting an innocent person is higher than that of doing the same with a guilty one. This condition always holds, as it is realistic to assume that public agents can distinguish between innocent and guilty individuals more accurately after the trial (when deciding on their conviction) than before (when deciding on their detention). Such compensation significantly reduces the standard for detention that minimizes the crime rate. First order condition is now: OO(ee,ee cccccccc ) zz(ww) pp iiii pp (ee )[1 II tt (ee cccccccc)] pp gg gg pp (ee )[1 GG tt (ee cccccccc)] cc pppp = 0 [32] The standard for detention that maximizes deterrence ee tt is hence such that pp gg gg pp (ee )[1 GG tt (ee cccccccc)] = pp ii ii pp (ee )[1 II tt (ee cccccccc)] [33] By contrasting expressions [33] and [12], we can see that compensating acquitted defendants reduces the standard for detention that maximizes deterrence, which in turn makes a corner solution easier to exist. Indeed, in a world with compensation every investigated individual is to be detained if: pp ii ii pp (ee )[1 II tt (ee cccccccc)] < pp gg gg pp (ee )[1 GG tt (ee cccccccc)] ee > 0 [34] [15]

16 Condition [34] is obviously less restrictive than [14]. Very low private costs of detention are not needed for condition [34] to be met. Compensation has the same effect on the standard for detention that maximizes deterrence as if the private costs of detention had been reduced to zero. 2. Standard for detention that minimizes social costs The total social costs derived from crime contain two main ingredients: the costs directly caused by crime and the costs of law enforcement (i. e. of detention and conviction). The standard for detention that minimizes the former ee is lower than the standard for detention that minimizes the sum of both of them ee. This standard ee will be lower (or a corner solution will be more likely) as: (1) the harm directly caused by crime h increases; (2) the social costs of detention cc decrease; (3) the social costs of conviction cc pppp decrease; (4) the private costs of detention cc decrease; (5) the number of acquitted innocent defendants II tt (ee cccccccc) increases; (6) the number of innocent individuals being investigated pp ii decreases; and (7) acquitted detainees are compensated for the harm suffered as a consequence of detention. By contrast, (8) increases of the private costs of punishment cc pppp can either lower or augment the optimal standard for detention. And it is not obvious which impact on this standard (9) increases in the number of acquitted factually guilty defendants GG tt (ee cccccccc), (10) in the probability of guilty individuals being investigated pp gg or (11) in the standard of conviction can have. Let us see. (1) An increase in the social net harm caused by each offense obviously increases direct costs of crime without affecting either deterrence or the costs of detention and conviction. Such increase makes thus more costly to raise the standard of detention above the standard of detention that minimizes crime ee, thereby pushing down the standard of detention that minimizes total social costs ee. h h ee OO ee >0 >0 < 0 [35] (2) An increase in the social costs of detention obviously makes the costs of law enforcement to rise, but it does not affect crime levels. If detention becomes more costly, without deterring aitional offences, the socially optimal standard required to detain people will obviously go up. ee cc cc ee > 0 [36] (3) Similarly, an increase in the social costs of conviction cc pppp makes the costs of law enforcement to rise, without deterring crime. As detaining people becomes more costly (because the expected social costs derived from it increase), the socially optimal standard for detention is to be higher. [16]

17 ee cc pppp ccpppp ee > 0 [37] (4) Increases in the private costs of detention will have two effects. On the one hand, as already noted, deterrence will diminish, thereby augmenting the direct costs of crime. On the other hand, the costs of law enforcement will increase as well, not only because each detention will become more costly, but also because more people will be detained and convicted. Both effects would push up the socially optimal standard for detention. Indeed, if the probability of being investigated, detained and acquitted is greater for innocent persons than for guilty ones, then ee cc cc ee > 0 [38] (5) Increases of the number of factually innocent defendants who are acquitted given a certain standard of evidence (for instance, because of an improvement in the evidence technology used in trial) boost deterrence, pushing down the standard of detention that minimizes both crime and consequently the direct costs of crime. Moreover, it lowers the costs from detaining and convicting individuals, thereby pushing up even more the standard for detention that minimizes these costs. If, as it is realistic to assume, the probability of being investigated, detained and acquitted is greater for innocent persons than for guilty ones, then II tt (ee cccccccc ) II tt (eecccccccc ) ee < 0 [39] (6) Increases in the probability of innocent individuals being investigated clearly lower deterrence, thereby augmenting the costs of crime and pushing up the standards for detention that minimize such costs. Furthermore, they increase the costs of law enforcement and, therefore, raise the socially optimal standard for detention. If, as already said, the probability of being investigated, detained and acquitted is greater for innocent persons than for guilty ones, then pp ii pp ii ee > 0 [40] (7) If compensation were a socially costless transfer of money, it would obviously reduce total social costs of crime by improving deterrence, without affecting the costs of law enforcement. If, on the contrary, compensation implies social (e. g. administrative) [17]

18 costs, then it will be worth it only if its deterrence benefits exceed such latter costs. For this to happen, the private costs derived from detention must be sufficiently high. (8) Increases in the private costs of punishment cc pppp can either lower or augment the socially optimal standard for detention. These increases always lower crime levels (and, consequently, direct costs of crime and, to some extent, even costs of detention and conviction, insofar as less people are detained and convicted), but they do it at a decreasing rate. There is thus one point where the benefits of an increase in the private costs of punishment are offset by the costs of such an increase. Up to this point, it is worth lowering the standard of detention. (9) The effects of an increase in the number of factually guilty defendants who are acquitted are not evident. On the one hand, this increase reduces the number of individuals who are convicted and, therefore, the costs of law enforcement. On the other hand, it also undermines deterrence, thereby raising not only the direct costs of crime, but also those of detaining and convicting people. It is not clear which of the two effects dominates, although we presume that the latter generally does. GG tt (ee cccccccc ) GG tt (eecccccccc ) ee > 0 [26] (10) The effects of an increase in the probability of factually guilty defendants being investigated are not clear either. On the one hand, such an increase augments the number of individuals who are detained and convicted, which raises the costs of law enforcement. On the other hand, it improves deterrence, thereby reducing not only the direct costs of crime, but also those of detaining and convicting people. It is not evident which of the two effects is stronger, although we presume that the latter may well be. pp gg ppgg ee < 0 [28] (11) It is neither obvious how increases in the standard of conviction can affect the standard of detention. VI. THE LAW The results we have reached are quite consistent with current legal rules. Let us analyze, for the sake of illustration, the standards of evidence governing detentions under U.S. American law. It must be pointed out that the amount of incriminating evidence required to detain individuals varies depending on several circumstances. There is thus not only one standard, but a range of them. The arguably strictest one has been established for the so called pre-trial detention. Although the U.S. Supreme Court has declared that probable cause, provided by the Federal Bail Reform Act of 1984, is a constitutionally permissible standard for [18]

19 pre-trial detention 17, the majority of state statutes require a showing of clear and convincing evidence of guilt 18. The second standard of the scale is that of probable cause, which is explicitly provided for in the Fourth Amendment with respect to seizures. Probable cause is thus required for ordinary arrests. The third standard is that of reasonable suspicion. The U.S. Supreme Court has stated that, in some circumstances, an officer may detain a suspect briefly for questioning although he does not have probable cause to believe that the suspect is involved in criminal activity, as is required for a traditional arrest... However, [it has] required the officers to have a reasonable suspicion, based on objective facts, that the individual is involved in criminal activity 19. This is a less demanding standard than probable cause and requires a showing considerably less than preponderance of the evidence 20. Lastly, the U.S. Supreme court has also stated that, in some cases (e. g. checkpoints permanently located in a highway in order to detect illegal aliens, sobriety checkpoint programs), state agents may carry out seizures even without any individualized suspicion against the affected individuals 21. This represents a corner solution. Everyone who is investigated (e. g. who goes through the checkpoint) suffers detention, if only for a very brief moment. Some quantum of individualized suspicion is usually a prerequisite to a constitutional search or seizure... But the Fourth Amendment imposes no irreducible requirement of such suspicion 22. Which is the rationale behind this scale? Why does the standard of incriminating evidence required for detaining people vary depending on the nature and the circumstances of the detention? 23 The U.S. Supreme Court has stated that the permissibility of a particular law enforcement practice is judged by balancing its intrusion on the individual s Fourth Amendment interests against its promotion of legitimate governmental interests 24. One can easily see, indeed, that the specific standard of incriminating evidence required to detain an individual depends to a great extent on the costs directly derived from depriving him of his liberty, which in turn depend on several factors, such as the duration of the restriction, the place where it is carried out, etc. The costlier the detention, the higher the standard needed for the detention to be lawful. The highest standard is prescribed for the most intrusive, stigmatizing, demoralizing and lasting kind United States v. Salerno, 481 U.S. 739, 755 (1987). Some authors, such as ALSCHULER (1986), at p. 566, and WILLIAMS (1994), at p. 366, argue that this standard of proof should be increased so that the guilt of the suspect is proved by clear and convincing evidence for him to be detained. See GOLDKAMP (1985), at pp , and WILLIAMS (1994), at p. 380, Brown v. Texas, 443 U.S. 47, 51 (1979). Illinois v. Wardlow, 528 U.S. 119 (2000). See United States v. Martinez-Fuerte, 428 U.S. 543 (1976); Michigan Department of State Police v. Sitz, 496 U.S. 444 (1990). United States v. Martinez-Fuerte, 428 U.S. 543, (1976). In this sense, the U.S. Supreme Court has declared that probable cause and reasonable suspicion are fluid concepts that take their substantive content from the particular contexts in which the standards are being assessed [Ornelas v. United States, 517 U.S. 690, 696 (1996)]; the probablecause standard is incapable of precise definition or quantification into percentages because it deals with probabilities and depends on the totality of the circumstances [Maryland v. Pringle, 540 U.S. 366 (2003)]. Delaware v. Prouse, 440 U.S. 648, (1979). [19]

20 of detentions. Probable cause is required for traditional arrests, which are usually not so costly for detainees and taxpayers as pre-trial detention. The reasonable suspicion standard is permissible when law enforcement officials must make a limited intrusion on the liberty of a person 25. And the crucial distinction between cases where reasonable suspicion is required and cases where it is not is the lesser intrusion upon the [individual s] Fourth Amendment interests 26. The harm directly caused by the offences intended to be prevented has also been taken into account in order to determine the appropriate standard. For instance, brief detentions carried out at sobriety, non permanent checkpoints without any suspicion have been considered permissible, considering not only the minimal duration and intensity of the intrusion on the individuals liberty caused by such detentions, but also the magnitude of the drunken driving problem 27. The effectiveness of detentions in preventing crime has also been considered in that respect. The U.S. Supreme Court has suggested that the more effective a detention program is, the lower the standard of evidence for detaining individuals may be. It has declared, for instance, that, given the physical and psychological intrusion visited upon the occupants of a vehicle by a random stop to check documents... the marginal contribution to roadway safety possibly resulting from a system of spot checks cannot justify subjecting every occupant of every vehicle on the roads to a seizure at the unbridled discretion of law enforcement officials 28. It seems common sense that the percentage of all drivers on the road who are driving without a license is very small, and that the number of licensed drivers who will be stopped in order to find one unlicensed operator will be large indeed... Furthermore... we find it difficult to believe that the unlicensed driver would not be deterred by the possibility of being involved in a traffic violation or having some other experience calling for proof of his entitlement to drive, United States v. Montoya de Hernandez, 473 U.S. 531, 541 (1985). Delaware v. Prouse, 440 U.S. 648, 656 (1979). In United States v. Brignoni-Ponce, 422 U.S. 873, (1975), the U.S. Supreme Court held that to allow roving patrols to stop all vehicles in the border area without any reason to suspect that they have violated any law, would not be reasonable under the Fourth Amendment. In United States v. Martinez-Fuerte, 428 U.S. 543, , by contrast, the U.S. Supreme Court declared that routine stopping vehicles at a permanent checkpoint for brief questioning of the vehicle s occupants is consistent with the Fourth Amendment, even in the absence of any individualized suspicion that the particular vehicle contains illegal aliens. The reason of the distinction lies in that the circumstances surrounding a checkpoint stop and search are far less intrusive than those attending a roving-patrol stop. Roving patrols often operate at night on seldom-traveled roads, and their approach may frighten motorists. At traffic checkpoints, the motorist can see that other vehicles are being stopped, he can see visible signs of the officers' authority, and he is much less likely to be frightened or annoyed by the intrusion Motorists are not taken by surprise, as they know, or may obtain knowledge of, the location of the checkpoints, and will not be stopped elsewhere [Aitionally] checkpoint operations both appear to and actually involve less discretionary enforcement activity. The regularized manner in which established checkpoints are operated is visible evidence, reassuring to law-abiding motorists, that the stops are duly authorized and believed to serve the public interest. The location of a fixed checkpoint is not chosen by officers in the field, but by officials responsible for making overall decisions as to the most effective allocation of limited enforcement resources. We may assume that such officials will be unlikely to locate a checkpoint where it bears arbitrarily or oppressively on motorists as a class. And since field officers may stop only those cars passing the checkpoint, there is less room for abusive or harassing stops of individuals than there was in the case of roving patrol stops. Moreover, a claim that a particular exercise of discretion in locating or operating a checkpoint is unreasonable is subject to post-stop judicial review (idem, at ). See Michigan Department of State Police v. Sitz, 496 U.S. 444 (1990). Delaware v. Prouse, 440 U.S. 648, (1979). [20]