How Do Criminals Make Decisions?

Rational Choice and Expected Utility Theory

Rational choice theory prescribes that individuals perform a cost-benefit analysis to make rational choices and achieve outcomes that fit their needs and desires. Consider an ultimatum game with you being a Responder. The Proposer has been given 100 dollars and proposed you take \(x\) of it (while they end up with \((100-x)\)). Would you accept the offer?

• Option 1: accept the offer.
  • Benefits: \(x\) dollars.
  • Costs: 0.
• Option 2: reject the offer.
  • Benefits: 0.
  • Costs: 0.

Being entirely rational, you would choose option one since the benefits outweigh the costs regardless of how much the Proposer would offer. Or in other words, you would rather end up with any amount of money than nothing. However, as one could imagine, human decision-making has much more to unpack.

First, economic theory introduces the term utility function \(U = f(X)\) that, technically speaking, reflects the total satisfaction/benefit an actor gets from the consumption of the commodities. For instance, an incremental dollar bill given to a billionaire has less utility than an incremental dollar bill given to someone with nothing. In the simple case, the utility function could be linear \(U(X) = X\) (Figure 2), where utility is the same as the absolute wealth obtained from the goods. More commonly proposed function is however \(U(X) = \sqrt{X}\), which includes the risk aversion. Risk aversion property will be discussed later in the post. The main point of the utility function is that not all risks, costs, and benefits carry equal weight in the decision-making process for different individuals or for the same individual over time.

Secondly, think about two scenarios. In the first one, the Proposer suggests a 50-50 split, and 95-5 (where the Proposer takes the bigger half) in the second one. Would your decision of acceptance be the same? Various experiments have shown that people are more likely to accept the offer in the first case but reject the offer in the second case. Moreover, Schweitzer and Gibson (2008)¹⁰ found that when people think they are mistreated, they become angry at the person responsible for it and feel justified in taking revenge. As discussed before, in both scenarios, a Responder initially starts with 0 and ends with a value greater than 0. So in terms of maximizing self-interest, both actions are considered optional. However, the problem is that humans are often not rational. We can feel unfairness or jealousy when given just 5 dollars out of 100, so we may reject the offer to “punish” the Proposer in return. This is the flaw of rational choice theory. It doesn’t account for emotions, cultural nuance, or unconscious behavior and instead shows how decisions should be made.

Thirdly, it is worth mentioning that actors often face uncertainty around events and actions in real life. Imagine somewhat different rules of a game. Now the Proposer flips a coin. If it comes up Heads, they split the money with \(x\) for you and \((100-x)\) for them, and if it comes up Tails, they take all the money. You can again either agree to flip the coin or reject it, and everyone ends with nothing. This is where the term expected utility \(\mathbb{E} \big[ U(X) \big]\) comes into play, which can be thought of as a sum of utility values weighted by their probabilities. Assuming \(U(X) = X\) utility function we have the following options:

• Option 1: accept the game offer.
  • Benefits: \(x\) dollars with the probability of 0.5.
  • Costs: 0 dollars with the probability of 0.5.
  • Expected utility: \(\mathbb{E} \big[ U(X_1) \big] = 0.5 \cdot x + 0.5 \cdot 0 = \frac{x}{2}\)
• Option 2: reject the game offer.
  • Benefits: N/A.
  • Costs: 0 with the probability of 1 (certainly don’t lose anything).
  • Expected utility: \(\mathbb{E} \big[ U(X_2) \big] = 1 \cdot 0 = 0\)

In this case \(\mathbb{E} \big[ U(X_1) \big] > \mathbb{E} \big[ U(X_2) \big]\), so the rational actor would still choose to play regardless of the proposed amount in the case of Heads.

Thus probabilities of benefits and risks (which could be either known or perceived) affect the decision-making. For example, in a series of experiments, Casey and Scholz (1991)¹¹ found that ambiguity around detection risk reduced college students’ willingness to commit tax noncompliance when detection risk was low but had the opposite effect when detection risk was high.

Lastly, apart from uncertainty, humans face other factors like imperfect information or time constraints that limit their rationality. When you want to buy the best sauce for pasta, you will not consider different sauces in every grocery store in your city. In the same way, when a burglar wants to rob a house, they probably will not explore each house in the neighborhood to find the target that fulfills all criteria. This reflects so-called bounded rationality, which suggests that humans make suboptimal decisions that are good enough for the current state of the environment, purposes, etc. Bounded decision-making has been shown in the review of sexual crimes by Pedneault et al. (2017)¹². They have shown that often the decisions were sub-optimal and were concerned for immediate positive and negative outcomes but discounted delayed consequences. For example, the selected crime location could be accessed by a third party, preventing the crime. These results also suggest that sexual offenders engage in myopic decision-making.

Furthermore, humans often make “intuitive” decisions using so-called cognitive heuristics (shortcuts), which may lead to systematic biases. Such heuristics save effort but can reduce the accuracy. For example, for residential burglars, environmental cues (the lighting, conspicuousness of the target, etc.) constitute rules of thumb for intuitive cost-benefit perceptions. Pogarsky and Piquero (2003)¹³ have shown that offenders with a short criminal history tended to reduce their perceived arrest risk after experiencing punishment, which reflects the gambler’s fallacy. The gambler’s fallacy is the incorrect belief that if a particular event occurs more frequently than normal during the past, it is less likely to happen in the future (or vice versa) when it has otherwise been established that the probability of such events does not depend on what has happened in the past. So it may look like such offenders are using the philosophy “If I was caught once, it’s doubtful that I will be caught again”.

Prospect Theory

Prospect theory describes how humans actually make decisions without rationality assumption. It prescribes that individuals make decisions based on expectations of loss or gain from their relative position (sometimes called the reference point). An essential element of prospect theory is that individuals are particularly averse to losing what they already have and less concerned about gaining. Given a choice of equal probability, individuals would choose to preserve their existing wealth rather than risk the chance to increase wealth.

Consider a classical Asian disease paradox. Imagine that the US is preparing for an unusual Asian disease outbreak, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed.

Problem 1:

• Program A: 200 people will be saved.
• Program B:
  • 1/3 probability that 600 people will be saved.
  • 2/3 probability that no people will be saved.

Which of the two programs would you prefer?

Problem 2:

• Program A: 400 people will die.
• Program B:
  • 1/3 probability that nobody will die.
  • 2/3 probability that 600 people will die.

Again, which of the two programs would you prefer?

If you paid close attention to the numbers and expected outcome, you could notice that programs use the same logic in both problems but are described differently. However, Tversky and Kahneman have shown that people are more likely to select program A in the first problem and program B in the second one (Tversky & Kahneman, 1981¹⁴). The main idea here is that humans have different preferences depending on their perceptions. An emphasis on gains evokes risk-averse behavior, whereas a focus on losses evokes risk-seeking behavior.

The hyperbolic shape of preferences for gains and losses can also be observed for delayed outcomes. Loughran and colleagues collected data from university undergraduate students who responded to a hypothetical scenario involving drunk driving (Loughran et al., 2012¹⁵). Participants had to indicate the estimated probability that they would drink and drive under the conditions described in the scenario. Scenarios involved several time points, starting from “tonight” up to “10 years from now”. They found that participants put more weight on close-in-time outcomes than the same outcomes in some observable future, whereas this was more pronounced for gains than losses. For example, when the benefit of drinking and driving was delayed by one week, the self-reported intention to drink and drive increased by nearly 10%. However, when the gain was postponed by one month, intentions to drink and drive increased by only 4%.

Whichard and Felson (2016)¹⁶ have related loss aversion property to the crimes that a priori have a low probability of success. For example, a target of a verbal attack which is facing the options to retaliate and possibly get physical injuries or to walk away and lose face, could go with the first option if they perceive losing face as a more significant loss. Another example would be the increased likelihood of homicide. Offenders are likely to anticipate a specific loss if they know that the victim or other witnesses can identify them. When offenders believe that allowing a witness to survive will lead to incarceration, homicide is more likely. The risk of severe punishment increases, but they take the risk to avoid a sure loss. The perception of inevitable loss is also expected to lead to lethal intent when people conflict with an armed or otherwise dangerous adversary. They are likely to take significant risks when it is “kill or be killed” and may engage in preemptive strikes when they anticipate an attack.

In the same way, the decision to resist the arrest may also seem irrational due to the estimated low chances of success. However, once the suspect perceives that they will be arrested, this realization can shift the offender’s reference point such that the impending arrest is a loss, thereby triggering the type of risk-seeking behavior that resisting arrest entails. However, as the authors pointed out, the decision to perform “senseless” or irrational choices can be influenced not only by the desire to avoid a sure loss but also by intoxication, mental impairments (as discussed in the Playing Games with Offenders section), or intelligence lack.

Additionally, a large body of literature suggests that individuals are more likely to make risky decisions when they are emotionally aroused. An example of such findings is work from Ariely and Lowenstein (2006)¹⁷. Recruited male undergraduate students were asked to evaluate the attractiveness of different sexual activities under the effect of high arousal achieved by masturbation. Results revealed that participants in the aroused group were more willing to engage in “date-rape” like behaviors and risky sexual practices than the control group. For example, they got significantly higher answer scoring for the questions like “Would you keep trying to have sex after your date says ‘no’?” or “Would you slip a woman a drug to increase the chance that she would have sex with you?” and lower scoring for the questions like “Would you always use a condom if you didn’t know the sexual history of a new sexual partner?”. Although it is important to note that the authors didn’t observe actual behavior, the questionnaire responses, so the results show what subjects think they would do in situations like these rather than what they did.

Notably, the decision to offend may be produced in a reinforcement way. If individuals experience that acts of crime do not result in legal punishment or feelings of shame or guilt, they may, over time, internalize the idea that such acts are acceptable or justifiable, thus, adjusting their perceptions about risks and costs. If the consequences of the action were overall positive, individuals would change their perceptions of rewards accordingly and would be more likely to engage in similar acts in the future. Vice versa, when individuals feel that an experience does not meet their expectations about the potential “thrill” or increased social status, they may internalize this and readjust their perceptions of benefits.