Criminal innovation and the warrant requirement: reconsidering the rights-police efficiency trade-off.

• Author: Jacobi, Tonja
• Position: III. An Economic Model of Criminal Innovation and the Warrant Requirement through Conclusion, with footnotes, p. 791-832

3. AN ECONOMIC MODEL OF CRIMINAL INNOVATION AND THE WARRANT REQUIREMENT

   This Part provides an economic model that demonstrates when the Police Efficiency Assumption will fail, or when LEOs will not be better be off in terms of their ability to catch criminals, if they are not required to obtain a warrant for an investigation than they would be if a warrant were required. To make this assessment, we analyze law-enforcement decisions in two different scenarios: one, under the "Warrant" condition, when a court has determined that a particular investigation is a search; the other, under the "Nonwarrant" condition, when a court has determined that the investigation is a nonsearch. For example, if a court finds that an investigative practice that LEOs widely consider to be a search is in fact a nonsearch, or vice versa, we can compare the effect of the rule change on police efficacy: if LEOs do not gain from the change away from the warrant requirement, the Assumption fails. In economic language, the Assumption fails if officers' expected utility (175) under the Warrant condition is greater than or equal to that in the Nonwarrant condition.

   Economic models enable us to formalize the incentives of both criminals and LEOs, and to examine the effect of different rules on their predicted behavior. Specifically, we use a game-theoretic model because we need to examine the decisions of both LEOs and the criminal as they influence each other. (176) The likelihood that LEOs will conduct an investigation depends upon the amount of innovation by criminals, because the latter impacts the chances that an investigation will find evidence. Likewise, the incentives for criminals to innovate will increase when LEOs are more likely to conduct an investigation. The utility of each actor depends on both its own decisions and those of the other actor.

   Most analyses of criminal innovation have not taken this approach and have simply looked at the criminal's decision whether to innovate. (177) These papers have treated a criminal's likelihood of being caught as a function of the amount of criminal innovation and the amount of resources society devotes to detecting crime. However, this view overlooks the fact that the decision by LEOs to investigate a particular crime is not fixed, but rather depends on the likelihood that an investigation will be successful--in other words, that it will reveal admissible evidence. Increased criminal innovation leads not only to a smaller chance of LEOs finding evidence if they conduct an investigation, but also to a smaller likelihood that LEOs will investigate at all, given the fact that they know criminals may innovate. (178) Thus, it is crucial to look at both of these effects when analyzing a criminal's decision whether to innovate. (179)

   This Part begins by discussing the variables that influence the decision by law enforcement whether to search and the decision by the criminal whether to innovate. It then lays out the games and solves them to determine the likelihood that LEOs will search and that the criminal will innovate. We are then able to specify the conditions under which the Police Efficiency Assumption fails.

   1. Criminal Utility

      Criminals act to maximize the utility gained from their crime. The model used here to analyze criminal decision making is adapted from the Becker model of crime. (180) That model analyzes a person's decision regarding the amount of crime to commit, comparing the benefits from crime to the expected cost of committing crime--the probability of detection multiplied by the punishment that comes with detection. (181) Our model is similar to Becker's model, but includes some important changes.

      First, we assume that the criminal has committed or is going to commit a single isolated crime. This means that the criminal's only decision is whether to innovate to cover up the crime. This assumption is in accord with what could be termed a "career criminal" or a "sophisticated criminal," who will definitely engage in a certain crime. The analysis thus applies only to crimes that will not be deterred by a transition from the Warrant condition to the Nonwarrant condition. Otherwise, the innovation and response effect we are trying to assess could be obscured by the possible benefits to society that may result in a move to the Nonwarrant condition through a reduction in the overall level of crime. (182) By examining a single crime that the criminal is determined to commit, we can set aside the possibility of crime reduction, which has been studied elsewhere. (183)

      Second, we assume that the criminal can engage in innovation that reduces the likelihood that LEOs will find evidence of crime in the event of an investigation. (184) This is the insight of the literature regarding criminal innovation. However, unlike that literature, which considers the amount of innovation to be a continuous variable that can be chosen by a criminal, (185) this model will treat innovation as discrete rather than continuous--the criminal either decides to innovate or not to innovate. The benefit of this assumption is that it more closely reflects the reality of the situation in which a criminal must decide whether to make an innovation in order to avoid detection for a particular crime. A bank robber cannot buy half of a mask and would not buy two masks for himself; a murderer does not need two silencers for his single gun, but also cannot purchase a silencer unless he pays the full price for it. A criminal in this situation is undoubtedly already using some nonzero amount of innovation; this preexisting innovation is encapsulated in the probability that LEOs will find evidence in an investigation. In Part IV, we consider what happens when innovation occurs on a sliding scale--when the choice is still whether to innovate, but there is a range of innovation options.

      Third, unlike in the Becker model, the likelihood that LEOs will investigate a crime is not fixed for any given crime, (186) but instead changes depending on whether the criminal innovates. The exact manner in which innovation changes the law-enforcement decision whether to investigate depends upon the incentives that LEOs face, but it is clear that LEOs will be less likely to investigate if criminals innovate because the likelihood of finding evidence is reduced. This interaction between the law-enforcement decision to search and the criminal's decision to innovate is central to the analysis and necessitates the use of game theory to analyze the situation.

      The criminal will aim to maximize his expected utility, (187) which will change depending on whether he innovates and whether LEOs investigate:

      The first utility matrix shows the relative costs of innovating and not innovating, for each possible law enforcement action. Because the criminal does not know whether LEOs will in fact investigate, he weighs the relative costs and benefits of innovating or not innovating within each shaded column, which models when LEOs have either investigated or not investigated, respectively. This calculation is analyzed in Part III.C.

      Criminal utility is a function of c, the cost of innovation, and a, the probability that LEOs will find a particular piece of evidence if they investigate, with the probability being high ([a.sup.H]) if the criminal does not innovate, and low ([a.sup.L]) if he does. The criminal's punishment if he is convicted has been normalized to equal 1; as such, c can be interpreted as the cost of innovation as a percentage of the amount of punishment the criminal faces.

      Other variables that may influence a criminal's level of innovation, such as the probability that the criminal will be convicted if the evidence is found and the amount of punishment a convicted criminal will receive, are omitted because they do not affect the general result. Unlike for LEOs, the criminal's payoffs are the same in the Warrant and Nonwarrant conditions, (188) so only one matrix is shown.

   2. Law-Enforcement Activity

      Unlike in most models of criminal innovation, which consider the likelihood of a law-enforcement investigation to be fixed, (189) LEOs in this model investigate only if it is in their best interests to do so. In order to assess the best interests of the police, we need to conceptualize law-enforcement utility. Unlike criminal utility, which is obviously the profits of crime, in these models it is standard to treat law-enforcement utility as constituted purely by an interest in effectively catching criminals. Thus, we disregard any other elements of job satisfaction or external interests, such as possibility of corruption. There is an opportunity cost for any law-enforcement investigation in terms of other investigations not undertaken or delayed; rationally, LEOs will prioritize investigations that are likely to lead to positive results. Viewed in these terms, it follows that LEOs will have an incentive to search less often if criminals innovate, because the likelihood of finding evidence in a search will be smaller.

      Similar to the criminal, LEOs will try to maximize their expected utility. Just as the criminal's utility depends on the actions of law enforcement, in turn law-enforcement utility will change depending on whether the criminal innovates. But because LEOs do not know whether the criminal has innovated, they weigh the relative costs of investigating and not investigating in each possible scenario. Thus in the second utility matrix, LEOs decide whether to investigate by comparing the expected payoffs for a given criminal action in each shaded row.

      Further complicating the situation here are considerations of the different payoffs to law enforcement first under the condition in which a warrant is required for the investigation, and then when no warrant is required:

      The variables z and w are constants that signify the cost of an investigation and warrant, respectively. An investigation is costly because of opportunity costs...