Bayesian Updating and Crime Research Paper

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Overview

Bayesian updating – the principle that individuals update prior beliefs in light of observed data according to probability rules – has important substantive implications for criminology. Theoretically, this principle may help formalize key causal mechanisms of deterrence, rational choice, social learning, symbolic interactionist, and developmental perspectives of crime. Empirically, recent research linking individuals’ perceptions of punishment risk to the objective certainty of arrest has developed formal models drawn from Bayesian updating. Such models help link macrolevel research on aggregate crime rates to microlevel research on individual risk perceptions and self-reported crime. This essay reviews empirical work on Bayesian updating of risk perceptions, points to theoretical and methodological challenges in this area, and outlines future research opportunities for perceptual dynamics and crime.

Introduction

Bayesian updating, or Bayesian learning, has become an increasingly important principle for specifying how human beings change their beliefs in light of new evidence. It has been applied to a variety of substantive topics, including machine learning, language acquisition, artificial intelligence, and dynamic systems. In criminal justice research, Bayesian inference has been applied to jury decision-making, as a rational way of accumulating evidence to reach a verdict (e.g., Robertson and Vignaux 1995). And in criminology, Bayesian updating has primarily been approached from a deterrence perspective, where individuals are argued to follow Bayesian processes when updating their perceptions of formal sanction risk in light of new evidence (Nagin 1998). Indeed, the link between Bayesian updating and deterrence theory is a useful place to begin the current essay.

Bayesian Updating, Deterrence, And Rational Choice

The deterrence doctrine is rooted in a rational decision-making framework. In his seminal work, Essay on Crimes and Punishment, the Italian Enlightenment scholar Cesare Beccaria ([1775] 1983:44) presented a utilitarian philosophy of criminal punishment that assumed actors weight pleasures and pains associated with behavior and seek to maximize pleasure and minimize pain. It follows that threatening citizens with punishments that are certain, swift, and proportional to the severity of crime would deter the public from violating the terms of the social contract. Beccaria argued that deterrence requires that punishment must be known in advance by all citizens, and therefore, written laws must clearly stipulate proscribed behaviors and unequivocally designate penalties for transgressors. Beccaria ([1775] 1983:44) further argued that formal sanction by the state is only effective insofar as citizens accurately perceive the cost of crime and apply this information to future offending decisions: punishments “ought to be chosen, as will make the strongest and most lasting impressions on the minds of others, with the least torment.”

The deterrence doctrine of the classical school was later formalized by neoclassical economists, who assume that actors maximize expected utility subject to constraints. Drawing on von Neumann and Morgenstern’s (1944) expected utility theory of risky decisions under uncertainty, Becker (1968:177) specified a utility function for criminal behavior that included the deterrent effect of punishment:

where E(U) refers to expected utility, p is the probability of getting caught as perceived by the criminal, (1 – p) is the perceived probability of getting away with crime, Y is returns to crime (both monetary and psychic), and F is the penalty. This utility function describes two states: getting caught or getting away with crime. When p=1, the criminal expects to get caught with certainty and, therefore, E(U) = U(Y– F); that is, the expected utility of crime is equal to the utility of the perceived returns to crime minus the punitive sanction (assuming that the criminal keeps her booty when caught). When p=0, the criminal expects to get away with certainty and, therefore, E(U) = U(Y); that is, the expected utility of crime is equal to the utility of the returns to crime. A person is assumed to commit crime when the expected utility of crime is higher than the expected utility of alternative legal pursuits (Taylor 1978). Moreover, Eq. (1) implies that, all else being equal, an increase in p, the perceived certainty of punishment will reduce the utility of crime, and thereby the probability of crime.

Both the classical and neoclassical models’ emphases on the actors’ perceived probabilities of punishment underscores the importance of information for deterrence and for decision-making in general. Because individuals’ perceptions of sanction risk are not exogenously determined but rather are endogenously produced through social interaction, a rational choice theory of deterrence and crime requires a theory of information. Such a theory would specify how information about sanction risks are communicated and disseminated to individuals. Here, Bayesian updating can provide a mechanism for risk communication which is consistent with rational choice theory. Understanding Bayesian updating first requires an understanding of the basics of Bayesian statistical inference.

Bayesian Inference And Updating

Based on the probability theorem posthumously published by Thomas Bayes (1701–61), Bayesian updating refers to the general principle that subjective beliefs should change given exposure to new evidence (Bayes and Price 1763). Bayesian updating provides a rational and principled way of combining prior beliefs with new evidence using Bayesian inference. It begins with two assumptions: (1) Subjective hypotheses about the world can be expressed as degrees of belief, which in turn, can be expressed in terms of probabilities ranging from 0 to 1. (2) Human beings are able to use probability distributions to represent uncertainty in inference. Given these assumptions, actors can use probability theory to compute the degree of belief of a hypothesis, h_i, given some observed data d, where h_i is a member of the set of mutually exclusive and exhaustive hypotheses H. Belief in hi prior to observing the data d is defined as the prior probability, denoted as P(h_i). The probability of observing datum d given that h_i is true is the likelihood, denoted P(d|h_j) . Bayes’ rule can then be used to derive our belief in h_i after observing the data, which is the posterior probability denoted P(h_i|d) :

Formula 2

where h_j ϵ H. The denominator is simply the sum of all possible hypotheses under consideration which ensures that the posterior probabilities of all hypotheses sum to one. This equation describes a rational updating process in which new evidence is combined with prior beliefs to yield a new subjective belief. The posterior probability P(h_i|d) is equal to the likelihood of the data given h_i is true P(d|h_j) times the prior probability P(h_j).

A simple example helps to illustrate how this equation produces Bayesian learning (see Table 1). For simplicity, assume there are only three prior hypotheses about the risk of arrest for burglary: certain arrest (P =1.0), 50/50 (P=.50) and certain to get away (P=0). The prior probability is .30 for certainty, .30 for 50/50, and .40 for getting away. Thus, given the opportunity, an actor would be expected to engage in burglary, since the highest probability is associated with getting away with the crime. The actor then observes new information or data, in which four of five burglars are arrested for the burglaries. Given the new data (that 80 % of burglars are arrested), the probabilities for our three hypotheses are as follows: .80 for certain arrest, .60 for 50/50, and .10 for getting away.

The updated probabilities become .522 for certain, .391 for 50/50, and .087 for get away (Table 1, column 3). Note that the highest subjective probability for the posterior is now getting caught (.552). Thus, all else being equal, after updating, the actor would be expected to refrain from burglary.

Bayesian inference assumes that the observed evidence or data are generated by some underlying process or mechanism, which has crucial implications for making inferences. The likelihood is based on a probability model of the mechanism by which the data were generated. In this way, Bayesian learning is a way of evaluating different hypotheses about the underlying process generating the data and making predictions about the most likely ones. For example, if the data on arrested burglars were generated from a random sample of the population of all burglars, and one views oneself as an average burglar, applications of Bayesian inference would be straightforward. However, if the data on arrested burglars were generated from a sample of very unskilled novice burglars, one would draw a different inference. Although the observed data are identical, this difference in the generation of the data will produce distinct likelihoods, altered posterior distributions, and different inferences. Thus, in applying Bayesian learning to substantive applications, careful attention must be paid to the generative process producing the data, a point returned to later in the essay.

The Heuristic Critique

Bayesian updating, as well as other rational principles of learning, has been subject to theoretical and empirical critique. Indeed, the emerging discipline of behavioral economics has as its focus the study of systematic ways human beings depart from rationality. Much of this research derives from the important work of Tversky and Kahneman (1974), who conducted a series of ingenious experiments that showed actors departing from rational updating in systematic ways, which they termed “cognitive heuristics” or “cognitive shortcuts.” The assumption is that human beings have a limited ability to process information cognitively, and therefore, must rely on cognitive shortcuts. Based on results of their social experiments, Tversky and Kahneman (1974) outline four heuristic rules that individuals use to form perceived risks, and which could bring about departures from a Bayesian learning process. The first, representativeness, refers to a tendency to rely on stereotypes, while ignoring information on population distributions. For example, people are likely to overestimate the probability a mother is black when told that she is a teenage mother, thereby forgetting or ignoring the extent to which whites are disproportionately represented in the population. In the case of certainty of sanction, individuals are likely to rely on stereotypes depicted in the media, in which criminals are caught and arrested. Research suggests that naıve individuals with no experience with the criminal justice system tend to overestimate the likelihood that they will be arrested if they commit crimes. Tittle (1980, p. 67) termed this “the shell of illusion.”

A second heuristic, availability, refers to the tendency to update based only on information that is easily or quickly retrieved from memory (Tversky and Kahneman 1974). Rare and mundane events are less likely to be recalled than common and vivid events. Moreover, the two could interact: events that are vivid, salient, and dramatic – as well as rare – could be brought to mind quicker than other events. The result can be bias due to differences in ease of retrieval, as vivid experiences or events trump other sources of information. For example, a dramatic event, such as being arrested for a crime, may swamp other sources of information in an individual’s estimate of rearrest. A third heuristic, anchoring, refers to a failure to adjust initial probability estimates sufficiently in light of new information. For example, when individuals are given an initial probability estimate that is arbitrary or even randomly assigned, followed by additional accurate information with which to update, their new estimates are consistently biased in the direction of the initial estimate (Tversky and Kahneman 1974). The estimates are anchored at the initial value, rather than adjusted properly in light of the new information. Applied to updating perceived risk of formal sanction, anchoring could lead to an effect opposite from that of availability. Individuals may fail to adjust risk estimates appropriately in light of new information and instead anchor on their baseline estimates. Tversky and Kahneman (1974) mention a fourth departure from Bayesian learning: the gambler’s fallacy. Stated simply, the gambler’s fallacy occurs when one assumes that a departure from what happens in the long run will be corrected in the short run. For example, if seven coin flips in a row have come up tails, one might think one is “due” for a heads. Applied to updating perceived risk, this might cause individuals who continuously get away with crime to think they are “due” for an arrest, or those who experience a string of arrests think they are “due” to get away with crime (Pogarsky and Piquero 2003).

Although experimental evidence suggests that actors do depart systematically from rational updating, some scholars argue that the departures are relatively small in magnitude, given the overall decision-making process. Thus, Bayesian updating of perceived sanction risk may be present net of cognitive heuristics. The next section summarizes related research on deterrence and updating risk perceptions.

Research On Deterrence And Perceptual Updating

Early empirical tests of Becker’s model used statistical models of aggregate crime rates, focusing on the deterrent effects of objective risk of punishment, using for example, risk of imprisonment (measured by imprisonment per capita) or risk of arrest (measured by arrests per crimes reported to police). Most notably, Ehrlich (1973) found deterrent effects of risk of imprisonment, but scholars criticized his simultaneous equation models for using implausible solutions to the identification problem – the problem of finding good instrumental variables to identify reciprocal effects between rates of imprisonment and rates of crime – such as assuming population age, socioeconomic status, and region have zero direct effects on crime (Nagin, 1978). Later work using aggregate data includes more plausible instrumental variables to address the problem of reverse causality and found deterrent effects. For example, Levitt (1997) employed the timing of mayoral elections as an instrument for the number of police per capita, under the assumption that such elections should have a direct effect on investment in the police force (as newly elected mayors seek to crack down on crime), but only an indirect effect on crime. For a review of aggregate deterrence research, see Nagin (1998) and Durlauf and Nagin (2011).

Tests of the deterrence hypothesis using aggregate data assume that aggregate clearance rates are good proxies for individuals’ perceptions of formal sanction risk, which is the key explanatory variable. A few economists remain uninterested in directly measuring individual risk perceptions and instead assume that the models need not describe perceptual or cognitive processes so long as actors behave “as if they are rational” and the models make good predictions. By contrast, most scholars view the measurement issue as an empirical question and welcome research on the relationship between aggregate rates of objective certainty of punishment and perceptions of the risk of sanction. Subjective expected utility models replace the objective certainty of sanction with a probability distribution of subjective probabilities. Such models are still rational models because the statistical mean of the subjective probability distribution is assumed to fall on the value of the objective probability (Nagin 1998). Empirical research from a subjective expected utility framework uses survey methods to measure perceived risk of punishment directly from respondents, rather than inferring it from behavior through the method of revealed preferences (e.g., Kahneman et al. 1997). These studies of individuals have the potential of linking subjective risk of punishment measured with survey data and objective risk of punishment measured with police clearance rates.

Early perceptual deterrence research by sociologists used cross-sectional data, eliciting self-reports of delinquent behavior and perceptions of risk of arrest in the same questionnaire or interview. These studies generally found small but significant deterrent effects for certainty but not for severity. That is, youth who perceive a high probability of arrest for minor offenses (like marijuana use and petty theft) tend to report fewer acts of delinquency. Such research was immediately criticized for using cross-sectional data in which past delinquency is regressed on present perceived risk, resulting in the causal ordering of the variables contradicting their temporal order of measurement (Paternoster 1987). These criticisms led to panel studies in which individuals are followed over short periods of time and both risk perceptions and self-reported crime are remeasured repeatedly.

The initial panel studies surveyed two waves of undergraduate students and estimated cross-lagged panel models. Here, self-reported delinquency is regressed on lagged delinquency plus lagged perceived risk and then perceived risk is regressed on lagged risk plus lagged delinquency. These studies found that both perceived risk and delinquency were fairly stable over a 6-month or 12-month period. Moreover, they found little evidence of a deterrent effect of the certainty of sanctions: net of lagged delinquency, lagged perceived risk of punishment was not significantly related to delinquent behavior. They did find support for the opposite effect: net of lagged risk, lagged delinquency exerted significant effects on perceived risk. Paternoster et al. (1982) called this an “experiential effect,” because it suggested that youth who experienced getting away with crime – arrest is fairly rare for the nonserious self-reported delinquent acts measured – reported lower risk of arrest. These findings were replicated on other two-wave panels of students. Furthermore, the results – a strong experiential effect and weak deterrent effect – were replicated in samples of disadvantaged adults in several cities at risk of serious crimes (Piliavin et al. 1986). The experiential effect was the first important empirical finding about the formation of individual risk perceptions. An experiential effect is consistent with a Bayesian updating model insofar as respondents have not been arrested between waves. If they had been arrested, that information must be included in any updating model.

Paternoster et al. (1985) found, for their two-wave panel of undergraduate students, experiential effects for minor property offender. They also found that students who were arrested between waves had higher perceptions of arrest risk. Horney and Marshall (1992) interviewed incarcerated felons and obtained their retrospective self-reported arrests and offenses. They computed, for a variety of offenses, the ratio of arrests to offenses and found that arrest ratios strongly related to perceived risk of punishment. This finding is consistent with a model of Bayesian updating. Subsequent research used prospective longitudinal designs to examine Bayesian learning of perceived risk. Pogarsky, Piquero, and Paternoster (2004) focused on changes in risk perceptions among a sample of high school students surveyed at the 10th and 11th grade. They found that students who experienced an arrest between the waves increased their perceptions of arrest certainty. This effect was most pronounced for offenders with an initially low-risk perception, which the authors attribute to these offenders having more room for change (i.e., a floor effect). Additionally, they found that individuals who reported higher peer offending had lower perceptions of risk, presumably because those friends avoided arrest. Stafford and Warr (1993) termed such a process vicarious punishment avoidance. This peer effect was greatest for nonoffenders, consistent with the idea that naive individuals have a “shell of illusion” (Tittle 1980:67) regarding police effectiveness that is eroded through vicarious experiences.

Two recent studies incorporate Bayesian updating of perceived risk into deterrence models of subsequent offending. Matsueda, Kreager, and Huizinga (2006) examined changes in risk perceptions and offending with longitudinal data of adolescents from high-risk Denver neighborhoods. They found strong support for a Bayesian learning hypothesis for both property and violent crime: lagged ratios of arrest per offense – which they termed, “experienced certainty” – were monotonically (positively) associated with perceived risk of arrest. In addition, respondents’ unsanctioned offenses were monotonically (negatively) related to perceived risk of arrest. They also found that perceptions of peer delinquency were negatively associated with perceived risk (see also Pogarsky et al. 2004). Each of these findings is consistent with Bayesian updating. Finally, Matsueda et al. (2006) also estimated a rational choice model of crime, finding that perceived risk of arrest was significantly associated with subsequent offending. Specifically, they found that, on average, a 10 % increase in perceived certainty of arrest was associated with a 3 % decrease in theft and violence. Lochner (2007) reported similar findings using data from the National Longitudinal Survey of Youth 1997 and National Youth Survey. He found that respondents in both surveys updated their risk perceptions in ways consistent with Bayesian expectations.

Offenders who got away with crime reported lower risk of arrest, and those who got arrested reported higher risks. Lochner (2007) also found that na¨ıve non-offenders held the highest perceptions of risk certainty. When comparing perceived certainty to actual offending, he strikingly found almost the exact same pattern as Matsueda et al. (2006): using the NLSY97 data, he found that a 10 % increase in perceived certainty of arrest was associated with a 3 % decrease in theft. The similarity of these results builds confidence in the deterrent effect of perceived certainty of arrest on future offending.

The most recent study of Bayesian updating, conducted by Anwar and Loughran (2011), examined serious juvenile offenders enrolled in the Pathways to Desistance Study. They found that offenders in their sample appeared to update their risk perceptions following a Bayesian model. Offenders who committed crimes and were arrested for them reported an average of 6.3 % higher-risk perceptions than those who committed crime but were not arrested. This is an important finding, as it suggests that risk perceptions remain malleable even among serious offenders, a population often written off as irrational or impulsive and thus outside policy intervention.

The weight of recent evidence thus supports Bayesian expectations when applied to updated risk perceptions and personal experiences of offending and sanctioning. As mentioned above, one might also ask if subjective sanction perceptions are rooted in objective rates of arrest and punishment. For example, does increased police arrest activity alter offenders’ subjective arrest perceptions? Interestingly, Lochner (2007) observed that the risk perceptions of his NLSY97 sample were fairly unresponsive to county-level arrestper-crime rates. Combined with his findings of individual experiential effects, the lack of a contextual effect suggests that proximate conditions are more important determinants of perceptual change than macro-contextual conditions. Kleck et al. (2005), in a phone survey of respondents in 300 counties, also found little correspondence between individuals’ estimates of police clearance rates and the actual clearance rates in those counties. However, Apel, Pogarsky, and Bates (2009) did find an association between changes in a school’s disciplinary regime and students’ perceptions of discipline, suggesting that individuals’ risk perceptions are responsive to contextual conditions in at least some instances. The limited and mixed findings in this area suggest that further research is required to connect objective sanction risk in a given geographic area to individual risk perceptions.

Extralegal Benefits And Costs

Research of the linkage between perceptual change and offending should also extend beyond formal sanctions. Theory and qualitative evidence suggest that other costs and rewards are equally, if not more so, related to criminal decision-making. As mentioned previously, Becker’s (1968) criminal utility model includes both subjective costs and benefits in criminal decision-making. This utility calculus lies at the heart of rational choice theories of crime (Clarke and Cornish 1985). The relative neglect of crime’s perceived returns, and how these perceptions are adjusted over time, is a serious omission both for etiological and policy reasons. Understanding crime’s perceived benefits will likely provide valuable insights for understanding criminal motivation, while also pointing to potential interventions that downwardly adjust individuals’ positive perceptions of crime over time.

In his phenomenological examination of violent and property crime, Katz (1988) provided perhaps the most detailed account of crime’s “seductive” psychic and social rewards. He explored the “sneaky thrills” of shoplifting and the social status associated with the “badass” gang member. Such perceived benefits are intimately linked to the criminal event and may override the certainty, celerity, and severity of perceived punishment. Indeed, Matsueda et al. (2006) found that the perceived excitement and “coolness” of offending were stronger predictors of crime than perceptions of arrest. Missing from their analyses, and generally overlooked in empirical analyses of criminal perceptions, are the origins and dynamics of crime’s perceived benefits as predicted by Bayesian learning.

Such analyses would appear particularly relevant for understanding individual trajectories of drug use. The objective risks of apprehension for drugs are low and likely swamped by perceptions of their psychic and social returns. In his classic Becoming a Marihuana User, Howard Becker (1953) described the learning process associated with marijuana initiation. In interviews of marijuana-smoking Jazz musicians, he found that users often entered their first marijuana experience uncertain of the drug’s effects. Moreover, marijuana’s psychopharmacological properties may result in potentially ambiguous physical effects, such as hunger, paranoia, dizziness, and euphoria, or no effects at all. Becker argued that the presence of more knowledgeable peers help the initiate translate these effects into a pleasurable experience worth repeating, or these peers may push the initiate to smoke again if he or she experienced no discernible effects the first time. In these ways, perceptions of fear and uncertainty are updated into fun and excitement. The change in marijuana’s perceived rewards upon initiation thus provides a particularly fruitful context for studying Bayesian updating.

Costs other than formal sanctions may also be important for understanding criminal decision-making. McCarthy and Hagan (2005) argued that the proximal fear of physical harm likely overrides perceptions of punishment for offending decisions. In their qualitative and quantitative study of street youth living in Toronto and Vancouver, they found that perceptions of danger deterred youth from theft, drug dealing, and prostitution. Interestingly, they found little evidence for the threat of legal sanctions, but, consistent with Matsueda et al. (2006), they did find that perceived excitement predicted theft and drug dealing. Note, however, that the cross-sectional nature of their data did not allow them to directly address the Bayesian updating hypothesis. More work is required to test if repeated exposure to crime and delinquency increases or decreases perceived danger.

Life-Course Transitions And Cognitive Change

The growth in life-course theories and research has opened up new avenues for understanding Bayesian updating processes. An axiom of life-course perspectives is that life events can meaningfully alter individual behavioral trajectories. Although the dominant explanation for how events become “turning points” in criminal trajectories is through external social control mechanisms (Sampson and Laub 1993), cognitive change is increasingly the focus of life-course criminology. Giordano et al. (2002) provided a symbolic interactionist theory that connects life-course transitions, cognitive transformation processes, and criminal desistance. Their central premise was that desisters are likely to reflect on their past and present circumstances and create new conventional identities. Life-course transitions, such as marriage, incarceration, and parenthood, then become “hooks for change” in this cognitive process. Interpreted from a Bayesian perspective, significant life events should provide new evidence by which prior perceptions are updated to shape future behavior. As Maruna (2001) points out, however, whether such life events positively or negatively affect self-perceptions is extremely difficult to predict. For example, a drug addict may interpret a friend’s overdose as (1) the final impetus needed to “get clean,” (2) unrelated to their own fate, or (3) a reason to use drugs to manage the resulting grief. The subjectivity of experience, and the meaning of experiences derived in contextualized social interactions, complicates an understanding of perceptual change and use of formal models of Bayesian inference. Identifying the origins of such heterogeneity is challenging but worth future investigation.

Conclusion And Future Directions

Under many guises, Bayesian updating remains an influential concept for criminological theory and research. Within the deterrence literature, researchers have consistently documented the experiential effect of crime on reduced risk perceptions, while also documenting an association between sanction perceptions and future offending. Rational choice studies have extended the study of perceptual dynamics to extralegal domains, including changes in perceived excitement, social status, monetary rewards, and fear of physical danger. More recently, life-course research has explored the impacts of life events on cognitive changes and desistance processes. All of these research strands continue to produce contributions for both criminology and the understanding of individual perceptual dynamics over time.

The obstacles facing perceptual research also provide opportunities for scientific advancement. As mentioned previously, a continuous challenge facing research in this area is disentangling experiential from perceptual effects. For example, an individual’s experiences in crime should change his or her perceptions of its costs and benefits, which should then impact his or her probability of future crime. Longitudinal designs are clearly necessary for distinguishing these reciprocal processes. One attractive strategy might be to design an experiment where individuals are randomly exposed to sanction risk information, such as local arrest statistics, to examine if their pretest arrest perceptions and behavioral intentions are updated upon receiving new information. Another potentially fruitful research avenue would focus on perceptual changes surrounding criminal onset. Prior to initiation, individuals must rely on less-than-optimal information sources – such as peers, the media, or experience with related behaviors – to formulate expectations for a novel behavior. But the inadequacy of prior information may result in actors initiating a behavior under extreme uncertainty. The situational contexts of initiation, and the physical experience of that event, are then highly influential in revising perceptions from uncertainty to increased clarity. The large amount of perceptual change potentially associated with initiation makes understanding this event critical for our knowledge of Bayesian updating. Although measuring the perceptions and contexts at the point of initiation would be difficult, it holds tremendous potential for broadening our insights of dynamic risk perceptions.

Future research is also required to order individuals’ perceptions of crime’s costs and benefits. Prior research has demonstrated that crime’s perceived extralegal costs and benefits often exceed the effects of perceived formal sanctions in predicting future criminal behavior. What is needed is research that identifies the relevant subjective perceptions of crime and helps rank order or weight these perceptions while also examining how such orderings may change over time. For example, the perceived social benefits of drug use may be a strong predictor of drug initiation, but upon initiation, such perceptions may be overridden by the perceived fun and excitement associated with getting “high.” Further, perceptions of pleasure may fade over time and be replaced by the perceived costs of heavy use. Bouffard (2007) has taken steps toward identifying preference orderings using subject-generated perceptions of criminal consequences, but more work is required to understand the dynamics of such orderings given individual experience.

More broadly, greater theorizing is necessary for the generative process of risk perceptions. Aside from personal exposure and vicarious experiences through peer networks, few studies have focused on the origins of offending perceptions and their changes over time. It is clear that non-offenders’ perceptions differ greatly from offenders’ perceptions, and that individuals transitioning from the former to latter typically experience substantial perceptual shifts. However, more research should center on the information sources associated with each status and how na¨ıve perceptions are updated or negated with offending decisions or experiences. Such investigations have substantial implications for interventions aimed at manipulating perceptions to prevent initiation (general deterrence), or increasing offenders’ perceived risks to prevent future offending (specific deterrence).

Finally, research should also continue to isolate the effects of salient life events (e.g., marriage, parenting, employment, military service, incarceration, etc.) on changing risk perceptions. Symbolic interactionist perspectives of desistance (Maruna 2001; Giordano et al. 2002) have taken strides in presenting theoretical models and qualitative evidence for how life events relate to cognitive transformation and desistance, but further quantitative evidence is needed to validate this line of inquiry and calibrate risk perceptions so that they may be formally analyzed using Bayesian inference. Prospective studies of sanction perceptions and prominent life-course transitions would add to an understanding of desistance while also testing the Bayesian learning hypothesis. Such investigations will provide greater clarity to the cognitive processes and decision-making associated with “knifing off” a criminal past and the construction of a conventional future (Maruna 2001).

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