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Scholars interested in decision making under risk have traditionally relied on the standard economic assumptions of expected utility (EU) theory (von Neuman and Morgenstern 1947) to specify the process by which individual actors make decisions. Under the EU framework – which serves as the foundation for deterrence and rational choice theories of crime going back to seminal work by Becker (1968) – an individual actor faced with a risky outcome is expected to select the specific behavioral action that yields the maximized anticipated payoffs. Importantly, the utility of behaviors are weighted by their probabilities of occurrence. The domain of the utility function in this model is absolute benefits and costs, whereby individual decisions of a course of action are dependent solely on the mathematical outcome of the difference between the probability of experiencing the utility of a behavior and the probability of experiencing disutility. Over time, however, researchers in behavioral economics and psychology have become increasingly aware that expected utility theory is not an adequate descriptive model of preferences under risk. For instance, consider the famous example posed by Tversky and Kahneman (1987) of an outbreak of avian flu that is expected to result in the death of 6,000 individuals. A national government has two plans to combat the pandemic: Plan A has a 100 % chance of saving 2,000 people, while plan B has a 1/3 chance of saving 6,000 people and a 2/3 chance of saving no one. Note that the expected utility in plan A (2,000 1 ¼ 2,000) and plan B (6,000 1/3 ¼ 2,000) is the same, but research indicates that individuals overwhelmingly select plan A, the more certain option (Tversky and Kahneman 1987). In other words, individuals do not make decisions based exclusively on the expected outcomes, but have a tendency to overweight more certain behavioral choices. Interestingly, Tversky and Kahneman (1987) demonstrate that this preference for certainty only holds when the risky outcomes are framed as losses, but does not hold when framed as gains. In other words, if the same hypothetical pandemic is framed as a 100 % chance of saving 4,000 lives (plan A; 4,000–1 =4,000) and a 2/3 chance of saving 6,000 lives (plan B; 6,000-2/3 = 4,000), individuals overwhelmingly select plan B – the more risky option. This suggests that preferences for risk can be situational depending on whether the individual is faced with the risk of gaining value or losing value.
The above examples are just two instances of violations of assumptions of standard expected utility theory, but many others exist. In response, several alternative models have been put forth that seek to address the shortcomings of expected utility theory. The most prominent model is prospect theory, developed by the cognitive psychologists Daniel Kahneman and Amos Tversky (1979). Prospect theory provides several alternative predictions that explain observed exceptions to the standard economic assumptions of expected utility theory. First, rather than choices being a function of absolute benefits and costs, value is determined by the gains and losses of an action relative to a reference point. Second, probabilities in the expected utility model are replaced by decision weights in prospect theory, which allows individuals to be more sensitive to expected losses than they are to expected gains (i.e., loss averse) and for marginal changes to be less impactful as they move away from the reference point (i.e., diminishing returns). Moreover, prospect theory posits that individuals have a tendency to underweight outcomes that are merely probable in comparison to outcomes that can be obtained with certainty. All of these predictions have received considerable empirical support, and prospect theory remains a prominent descriptive framework for the way people make decisions in the face of risk and uncertainty (Starmer 2003).
Despite its utility in understanding decision making under risk, few studies to date have applied prospect theory to the study of crime (see Loughran et al. 2011). This research paper outlines the value of incorporating prospect theory to the study of crime and deviance and to rational choice and deterrence theories more specifically. The paper begins by briefly specifying the standard economic assumptions prevalent in expected utility theory. Next, it provides a brief overview of violations to these standard economic assumptions, findings that were pivotal in Kahneman and Tversky’s development of prospect theory. Finally, the paper then describes the core tenets of prospect theory, and its descriptive advantages for understanding choices when faced with risky and uncertain situations, and concludes by highlighting some important questions that prospect theory raises about criminal decision making.
Fundamentals Of Expected Utility Theory
Expected utility theory is a model of decision making under risk, where each behavioral action leads to a set of outcomes that can be either beneficial or costly to the actor. Importantly, the probability of each outcome is known, which enables individuals to make informed decisions when faced with risk. The core principle of expected utility theory is based on the standard economic assumption that individuals select the behavioral option that has the maximum expected utility. More specifically, the utility of each outcome is weighted by their associated known probabilities, and individuals choose the behavioral action that has the highest weighted final sum (Luce and Raiffa 1957).
They key components of expected utility theory have been incorporated into prominent criminological perspectives such as rational choice and deterrence theories (see Becker 1968; Cornish and Clarke 1986). From these theoretical perspectives, an individual is expected to offend if p * U(Benefits) – p * U (Costs) > 0, where U(*) is a utility function that standardizes various costs and benefits from offending into comparable units, and p is that perceived probability (between 0 and 1) of experiencing an outcome. This model suggests that an individual will decide to commit a crime if the benefits from offending outweigh the potential costs. The known probabilities p are important in this model: For instance, as p increases with regard to the costs of crime, the net benefits of offending necessarily decrease. In other words, the deterrent effect of certainty on offending increases monotonically with increments of risk. What constitutes a “benefit” and “cost” of crime varies considerably across perspectives. For instance, early work in deterrence and rational choice focused almost exclusively on monetary gains and costs deriving from formal sanctions (Becker 1968), while more recent works have broadened these choice perspectives to allow benefits to include things such as prestige and social status, and costs to include things such as disappointing loved ones, moral regard, and shame (Cornish and Clarke 1986; Grasmick and Bursik 1990; Paternoster 1989). In general, the calculus of rational choice is generally not well understood, but there is strong evidence that the risk of detection, or the ostensible weight in this rational choice calculus, is associated with offender decisions (Nagin 1998).
Regardless of the outcomes that constitute benefits and costs, the process outlined in expected utility theory is thought to be a descriptive model of how individuals actually behave in risky situations. Importantly, the expected utility model makes several important implications with regard to the decision-making process. For instance, expected utility theory does not specify the functional form of the decision-making process. In this way, it is at least implied that utilities and their associated probabilities affect choices in a linear fashion, where a 10 % increase in the probability of an outcome has the same marginal effect at all points on the probability continuum (an increase in the certainty of arrest from 10 % to 20 % has the same marginal effect as an increase from 60% to 70 %). Further, the expected utility model assumes that individuals treat benefits (gains) and costs (losses) in a similarly weighted manner. In monetary terms, a $100 gain that may be accrued by engaging in a behavior is treated the same in an individual’s calculus as a $100 loss.
The core tenets of expected utility theory are prevalent throughout the field of criminology. However, research in behavioral economics has identified several situations where the predictions of expected utility theory are violated.
Violations Of Expected Utility Theory And The Foundations Of Prospect Theory
Kahneman and Tversky (1979) begin their seminal paper on prospect theory by presenting the results of several laboratory experiments that involve hypothetical choices. Many of their findings explicitly contradict the assumptions of expected utility theory, suggesting that individuals appear to make irrational decisions under some circumstances of risk. However, Kahneman and Tversky (1979) were able to demonstrate that the apparent irrationality has considerable consistency. Accordingly, they attempted to develop a description of decision making under risk that can explain the following observations:
- People do not tend to make choices in terms of their net utility as predicted by expected utility theory, but instead code the outcomes of behavioral choices as gains or losses relative to a reference point. The reference point usually corresponds to one’s current assets or the status quo but can also include one’s expectations, and represents the zero point on one’s value scale. Accordingly, the expected utility of a choice is thus evaluated as deviations from this subjective zero scale, such that “the same level of wealth… may imply abject poverty for one person and great riches for another – depending on their current assets” (Kahneman and Tversky 1979, p. 277). Put simply, objective benefits and costs of behavioral choices can have considerably varied effects across individuals, depending on one’s initial asset position.
- Because individuals encode outcomes in terms of gains and losses relative to reference points, the framing of choice options can be critical in an individual’s decision. Take, for instance, the avian bird flu example presented in the introduction, where individuals are asked to select one of two programs seeking to prevent spread of the disease. We noted that when the outcomes are framed as lives saved, respondents overwhelmingly select the sure gain of 2,000 lives rather than the 1/3 chance at saving 6,000 lives. When framed as lives lost, however, individuals tend to reject the sure loss of 4,000 deaths and prefer to take the risk. This relationship can be interpreted as support for the idea that individuals are riskaverse with regard to gains and risk-seeking with regard to losses, but Starmer (2003) argues that it is just as important to understand how the consequences are interpreted. In other words, though the 4,000 lives lost is objectively the same in both situations, the framing of the scenario influences whether they are interpreted as gains or losses. Accordingly, Kahneman and Tversky go to some length to explain this in their discussion of editing and heuristics.
As will be detailed more below, prospect theory suggests that individuals edit choice prospects using a variety of heuristics, prior to evaluating their utility. One of the most important editing processes, discussed above, is the coding of outcomes as gains or losses relative to a reference point. Kahneman and Tversky go on to note that, though the reference point is typically one’s current assets, “the location of the reference point, and the consequent coding of outcomes as gains and losses, can be affected by the formulation of the offered prospects.. .” (Kahneman and Tversky 1979, p. 274, emphasis added). Thus, the framing of behavioral choices can determine an individual’s reference point and, in turn, whether prospects are interpreted as gains or losses. This framing effect has been demonstrated across numerous experimental studies (McNeil et al. 1982; Tversky and Karhneman 1986).
Situational characteristics can play a major factor framing the way that individuals code and evaluate prospects when making decisions. Importantly, as Levy (1992) notes, such framing effects can often be subjective, particularly when there is ambiguity with regard to the status quo. In any sense, the framing of behavioral choices can play a major role in offender decision making. For instance, framing and the use of availability heuristics may explain why individuals systematically overpredict the certainty of arrest in self-report studies of offending. Much of individuals’ knowledge about the crime comes from media accounts, which can cause individuals to perceive the status quo on the certainty of arrest to be high. When faced with situations where offending is possible, however, individuals may develop a new status quo from which to analyze behavioral choices. Similarly, an individual who is socializing in a group where the perceived status quo is conformity, he/she is likely to hold conforming values as well. If that same individual is present in a group that espouses pro-delinquent values, then that individual is likely to develop a new status quo and make behavioral choices that are relative to this new reference point (Warr 2002). The point is that many of the field’s most dominant explanations of crime emphasize the importance of subjective beliefs – such as perceived certainty of arrest or social reinforcement – but often treat such beliefs as static across different situations. A more nuanced understanding of the roles of subjective beliefs may be garnered by understanding how situations frame prospects and influence the decision-making processes of individuals (see Manski 2004).
- Though Kahneman and Tversky (1979) note that individuals make behavioral choices based on changes from a reference point, they also find evidence that individuals treat gains differently from losses in two ways. First, individuals tend to be risk-averse when it comes to gains and risk-seeking when it comes to losses. A person is risk-averse if he/ she prefers a certain prospect (x) to any risky prospect with expected value x. A person is risk-seeking if he/she prefers to accept risk to secure benefits or avoid losses. For instance, a person is considered risk-averse if they prefer $50 guaranteed to a 50 % chance of winning $100, while a person is risk-seeking if they prefer a 50 % chance of winning $100 to $50 guaranteed. The results of Kahneman and Tversky’s experiments explicitly contradicted the descriptive model of expected utility theory with regard to the differential treatment of gains and losses. When faced with the hypothetical prospect of gaining money, Kahneman and Tversky (1979) found that 82 % of participants preferred the certain outcome of gaining $3,000 to an 80 % chance of gaining $4,000 and a 20 % chance of gaining nothing. Note that the expected utility is actually higher in the latter option ($3,200 vs. $3,000), but respondents are overwhelmingly risk-averse and prefer the more certain, although smaller, payoff. Conversely, when faced with the hypothetical prospect of losing money, individuals are substantially more risk-seeking. Kahneman and Tversky show that 92 % of participants preferred to gamble on an 80 % chance of losing $4,000 and a 20 % chance of losing nothing over a certain loss of $3,000. Again, in this scenario, individuals chose the option with the lower expected utility, which directly contradicts the assumptions of expected utility theory. This pattern has been demonstrated across a wide range of behaviors (see Edwards 1996).
- Kahneman and Tversky (1979) also find that individuals treat losses different than gains in that (i) the utility functions of gains and losses differ such that the shape of the utility function is concave for gains but convex for losses and (ii) that the utility function is steeper in the domain of losses. Tversky and Kahneman (1992) interpret these as two general properties of decision making under risk: diminishing sensitivity and loss aversion. “Diminishing sensitivity holds that the psychological impact of a marginal change will decrease as we move further away from a reference point” (Starmer 2003, p. 128). Thus, with a reference point of zero, the difference between a gain of $10 and $20 will seem larger than the difference between a gain of $110 and $120. This trend is known in the economic literature as diminished marginal utility. For losses, the same principle is known as diminished marginal disutility and also has implications for offender decision making – i.e., the marginal change in increasing the severity of sanctions from 1 year to 2 years would have a larger impact on offending than the increase from 11 years to 12 years.
The second property (ii) discussed with regard to the utility function of gains and losses, loss aversion, is the idea that “losses loom larger than corresponding gains” (Tversky and Kahneman 1992). This is to say that individuals place a higher value on a good that they already possess than to one that they do not. Thus, when presented with a scenario where there is a 50 % chance of winning $50 and/or a 50 % chance of losing $50, Tversky and Kahneman have demonstrated that individuals find the latter option distinctly unattractive.
- As noted in the introduction, one finding of Kahneman and Tversky (1979) that contradicts expected utility theory is that individuals have a tendency to overweight outcomes that are certain and underweight outcomes that are merely probable, what Kahneman and Tversky label the certainty effect. For example, consider choosing between an 80 % chance of receiving $4,000 and a 20 % chance of gaining nothing versus a certain gain of $3,000. Notice that the expected payoff is higher in the former option (EU ¼ $3,200), but research indicates that individuals are more prone to select the second option. Moreover, research also indicates that individuals have a tendency to treat extremely likely, but uncertain, outcomes as if they are certain, which is known as the pseudocertainty effect (Tversky and Kahneman 1986). The point is that individuals have a tendency to weight probabilities near 0 and 1 greater than would be anticipated in expected utility theory. Consequently, studies have also contradicted the assumptions of expected utility theory that utilities of risky outcomes are weighted linearly by their probabilities. For instance, a change in the probability of experiencing a loss from .10 to 0 is weighted more heavily than a change from .70 to .60.
Fundamentals Of Prospect Theory: An Alternative Model For Choice Under Risk
It is apparent that several of the central predictions of expected utility theory are regularly violated in instances where decisions are made under risk. Prospect theory attempts to incorporate these observed violations in order to provide a more descriptively valid theory of risky decision making. In prospect theory, choice is modeled as a two-phase process: the editing phase and the evaluation phase. In the first phase, prospects are “edited” using a variety of decision heuristics. The purpose of the editing phase is to conduct a preliminary and simple analysis of the offered prospects. By using various heuristics, individuals conduct several operations that transform outcomes and their associated probabilities to allow for a simple evaluation of the prospects. Kahneman and Tversky (1979) note that there are several mental operations that occur in the editing phase for each individual prospect: coding which defines each prospect as either a gain or loss relative to a neutral reference point, combination which combines the probabilities of identical outcomes, and segregation which segregates the riskless components of prospects from the risky components. Moreover, Kahneman and Tversky (1979) also note that individuals compare two or more outcomes in the editing phase using the following: cancellation which discards the common components of different prospects, simplification which is rounding probabilities, and detection of dominance which discards outcomes that are easily dominated by other outcomes.
The editing phase is critical in the decision-making process and is one of the most distinguishing features of prospect theory. It allows individuals to prepare outcomes and their associated certainties of occurrence prior to evaluation. Note that the editing phase in prospect theory incorporates many of the observed anomalies to the standard expected utility theory. For instance, reference points become the relative point at which individuals evaluate gains and losses rather than simply assessing the absolute cost and benefits of behavior. Moreover, prospect theory allows for reference points to be determined not solely by one’s current assets but also by one’s expectations and by the way in which the prospects are framed. Further still, and contrary to expected utility model, the preference ordering of outcomes “need not be invariant across contexts, because the same offered prospects can be edited in different ways depending on the context in which it appears” (Kahneman and Tversky 1979, p. 275). These features of prospect theory can make complex choice situations difficult to predict, as the editing process is influenced by the norms and expectations of the individual actor (Tversky and Karhneman 1986). Because of this, Kahneman and Tversky (1979) largely focus on the second phase of decision making, but it remains noteworthy that certain individual and contextual factors can reasonably be used to predict that editing process and the determination of status quo reference points.
Once the editing phase is complete, choices among edited prospects are determined in the evaluation phase. In this phase, individuals select the maximized edited prospect as determined by a simple decision-weighted utility function that transforms probabilities into weights that impact the overall value of the prospect and evaluates the subjective value of each outcome relative to a reference point that serves as a zero point on a value scale (see Kahneman and Tversky 1979, p. 275). Hence, value is determined by the deviation of each outcome from the reference point.
Rational Choice and Prospect Theory, Fig. 1 Value Function According to Prospect Theory (Kahneman and Tversky, 1979)
In prospect theory, outcomes are evaluated using a utility function shaped like that presented in Fig. 1. Notice that this function has several important qualities. First, the function is slightly kinked at the reference points (Starmer 2003), where xi ¼ 0. Another quality of this function is that it is concave for gains and convex for losses. These properties are important as they indicate diminishing sensitivity as described above – i.e., the psychological impact of a marginal change decreases the further one gets from the reference point. A third quality of this value function is that it is steeper in the domain of losses, which implies that individuals tend to be more loss averse. Thus, many of the properties of prospect theory’s value function have been observed in experimental assessments of decision making under risk.
The decision-weighting function specified in prospect theory also possesses some important qualities. It should be noted that decisions weights are inferred from choices in a manner that is similar to probabilities in expected utility theory, but these decision weights are not probabilities and should not be interpreted as such. Instead, the “decision weights measure the impact of events on the desirability of prospects, and not merely the perceived likelihood of the events” (Kahneman and Tversky 1979, p. 280). This distinction is important because it allows the decision weight to be influenced by factors other than the probability of an outcome. For instance, ambiguity, or the uncertainty about the level of certainty one has with regard to the outcome, can also impact the decision weight. As will be noted below, this feature of the decision weight is an important quality of prospect theory and has important implications for understanding the decision to offend (Loughran et al. 2011).
The decision-weighting function has several other important features. For instance, Kahneman and Tversky (1979) propose a weighting function where “large” probabilities are underweighted and “small” probabilities are overweighted. In fact, the function is not defined for probabilities at or near 0 or 1, because “people are limited in their ability to comprehend and evaluate extreme probabilities” (Kahneman and Tversky 1979, p. 282). In particular, individuals are likely to completely ignore unusually small probabilities and exaggerate extremely high probabilities. Kahneman and Tversky (1979) note that this has another important implication: It suggests that the decision weight function is relatively shallow in the midpoints, but changes abruptly near the endpoints, which is consistent with the certainty effect described above.
In summary, prospect theory is an important alternative description of decision making under risk, because it is well suited to account for many of the observed violations of expected utility theory. The certainty effect, framing effects, loss aversion, ambiguity in uncertainty, and the finding that utility is evaluated as deviations from a reference point can all be explained by prospect theory, and this theoretical perspective is highly influential in understanding social behavior (Levy 1992).
The Role Of Prospect Theory In Criminology
Research in behavioral economics and psychology has consistently found support for the general tenets of prospect theory. Nevertheless, the importance of prospect theory, with few exceptions (see Loughran et al. 2011), has not been integrated into criminology. Indeed, models testing offender decision making have relied almost exclusively on the descriptive model of rational choice theory, a model of decision making under risk that we know is violated in many circumstances. Given the shortcomings of expected utility theory in predicting decisions under risk, prospect theory has the potential to be highly influential in understanding offending behavior.
Loughran and his colleagues (2011, 2012b) have begun to integrate prospect theory into deterrence theory, and the results of their studies have suggested that the predictions of prospect theory fit offending data better than those derived from expected utility theory. To be sure, most studies assessing the relationship between perceived certainty of arrest and probability of offending have, at least implicitly, assumed that the relationship is linear. However, as noted above, prospect theory predicts that the relationship between certainty of risk and behavior is nonlinear, and laboratory studies have indicated that individuals only begin to weight potential losses when the certainty of experiencing an outcome is around 30 %. This was described as a “tipping effect” whereby probabilities below this were essentially underweighted or disregarded all together. This, of course, has significant implications for deterrence theory, as it challenges the functional form of the certainty offending relationship that marginal changes in certainty affect probability of offending in a linear fashion. In support of prospect theory, Loughran and Colleagues (2012b) showed that individuals tend to weight perceived probabilities of risk non-linearly. Specifically, perceived risk only had a deterrent effect when the probability of arrest exceeded a threshold of .3 to .4, and there was a substantial increase in the marginal effect after that. Thus, Loughran et al.’s findings provided empirical support for the nonlinear probability weighting proffered by prospect theory.
In another study, Loughran et al. (2011) extended prospect theory to assess if ambiguity, or uncertainty about the true probability of detection (Camerer and Weber 1992), in the certainty of arrest was important in understanding criminal decision making. Though not a formal test of prospect theory per se, the results were consistent with framing effects. Using two different data sources, they found that ambiguity in the perceived risk of detection was a deterrent when the perceived risk was low, yet actually encouraged offending when the risk was higher.
These are the only two studies to date that have incorporated prospect theory into the study of crime. Though underdeveloped given the empirical support for prospect theory and the important role of choice in criminological theories (Akers 1990; Cornish and Clarke 1986; Paternoster 1989), this gap in the literature does provide avenues of future research that can shed considerable light on our understanding of offending behavior.
For instance, the idea that individuals make decisions based on gains and losses from a reference point raises some interesting questions regarding the decision to engage in crime and has considerable implications for criminological theory, beyond the commission of economic crimes. For example, the cost of experiencing an arrest and the gains in social status incurred when engaging in crime are typically measured as objective and absolute benefits/ costs, and researchers rarely model these costs and benefits as losses and gains relative to a reference point (i.e., one’s current social status among friends). Moreover, the predictions of prospect theory also raise important questions regarding the measurement of crime and delinquency in self-report questionnaires, suggesting that the framing of questions may influence responses and that individuals may have a tendency to utilize response strategies that are highly contingent on the status quo rather than their own subjective beliefs (see Loughran et al. 2012a, forthcoming).
It may also be useful to understand how diminishing sensitivity and loss aversion affect individual decisions to offend. Many criminological theories highlight the importance of rewards to crime (Akers 1998; Cornish and Clarke 1986), but prospect theory would make distinct predictions regarding the functional form on the relationship between rewards and offending. Does the proportion of one’s deviant peers affect delinquency in a linear fashion? Or would the data suggest that delinquent peers have a diminishing marginal utility when it comes to promoting deviance? Loss aversion suggests that individuals may be more influenced by the threat of losing social status and material assets than they are by the potential or gaining such things. Further, loss aversion predicts that individuals are more risk-seeking after experiencing losses in their assets. How does this affect decisions to participate in illegal markets? Are individuals more likely to initiate into or increase their involvement in markets after experiencing losses to income (both legal and illegal)? These are just two examples, but diminishing sensitivity and loss aversion have implications for a wide range of criminogenic influences.
Another avenue for future research in the role of prospect theory and crime concerns certainty in decision weighting. Research in deterrence theory has found only a weak relationship between perceived likelihood of arrest and offending (Pratt et al. 2006), leading some scholars to question whether individuals consider the threat of sanctions before deciding to offend and the rationality of offenders. But criminogenic situations are often such that individuals have almost certain gains (stealing money) but relatively less certain losses (being arrest). In this way, it may not be that individuals are irrational in their decision making or fail to consider potential costs, but rather are attracted to the more certain gains that are involved in the risk. In other words, though individuals have perceived that the cost of an arrest is relatively high, this disutility maybe underweighted because of the lack of certainty in experiencing the loss, relative to the gains.
Deterrence and rational choice theories continue to be two of the most prominent perspectives in criminology. Though our understanding of offender decision making has unquestionably advanced in recent years, most research assessing criminal choice is based off of the standard economic assumptions of expected utility theory that have repeatedly been shown to be violated in situations involving choice under risk. Prospect theory is an alternative model to decision making under risk that can explain many of these shortcomings (Tversky and Kahneman 1992). To date, prospect theory has not yet been widely integrated to the study of crime and delinquency. While this is unfortunate, it does provide a plethora of opportunities for scholars interested in offender decision making to apply the predictions of prospect theory – which oftentimes differ greatly from predictions derived from traditional expected utility theory – to the decision to engage in criminal and deviant behaviors and in turn further advance the field’s understanding of criminal choice.
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