Erica Lee and Emily Yeh

We build off of the model from Groff's report, Simulation for theory testing and experimentation, with an agent-based model of Citizens in CrimeWorld, an environment where each Citizen has their own characteristics and behavioral rules, including the Citizen’s likelihood of committing crimes. Comparing our results to Groff's, we observe that our results behave qualitatively similarly. By extending Groff's experiment, we implement a CrimeWorld with punishment for committing crimes and find that the number of crimes committed is lowest when offending Citizens are caught and punished by losing half of their wealths.

Research consistently shows that people living in poverty commit more crimes than people living in high-income households.⁶ This can be due to a variety of factors, such as employment accessibility, residential instability, and general distrust, but the most commonly cited factor is income and wealth inequality⁸ which is the factor we investigate in our model. Our model is based off of one generated by Groff,⁵ in which agents interact in a world based on various rules: no crimes may be committed in the presence of authority, and criminals only commit crimes if certain conditions, which are described in subsection A, are satisfied. In our model, the agents are called Citizens and they inhabit a graph-like world called CrimeWorld, where each node is a street intersection. Each Citizen has several behaviors: they spend approximately 8 hours (the length of a work day) of their day moving around randomly in CrimeWorld, after which they return to their designated home and "sleep." They move randomly in one of the four cardinal directions for each time step. They can have two different roles: some Citizens are offenders (agents who commit crimes) and some are police (agents who prevent crimes). The offender agents share sets of characteristics, and for each time step, these characteristics help to determine whether they commit a crime or not. We will explain the decision-making process that offenders go through in Subsection 1A.

We would like to acknowledge that we base our model off of Groff's⁵ model, as opposed to replicating it completely. This is because Groff's model is built on the routine activity theory, which asserts that if the frequency of convergence between offenders, guardians, and targets increases, crime rates may increase even if the absolute number of motivated offenders remains constant. In other words, as individuals spend more time away from home, crime rates increase. Since we are not interested in creating a model based on this theory, but rather creating as accurate a model of crime as possible, we decided to use the parts of Groff's model that are relevant to this goal and unrelated to routine activity theory, leaving out the rest.

For each time step, 20% of Citizens have the potential to commit a crime. This proportion is based on data cited by Groff, which states that the proportion of civilians who have committed a crime in Seattle is approximately 20%.⁹ If one of these Citizens' wealth is negative, however, they automatically commit the crime, instead of going through the decision-making process explained below. Citizens who are at home during a given time step cannot rob others, nor can they be robbed.

According to Groff's experiment,⁵ a variety of factors affect an offender's decision to commit a crime. Consider several agents at a single node; some might be police and the rest might be offenders trying to find a target amongst each other. The first factor the offenders must consider is whether there are police at the node, since no crimes may be committed in the presence of a police officer. However, if there are no police officers, the offenders must consider several other factors, which are summarized in Figure 1.1.

Figure 1.1. An offender's decision tree⁵; how an offender decides whether to commit a crime.

Figure 1.2. An offender's decision tree, as modified from Groff's original decision tree.

As Figure 1.1 indicates, if there are no police officers in a node, the second factor the offenders must consider is the guardianship of other agents present - a variable represented by G.

G depends on two other variables. N_agents is the total number of agents present at a given node, and 2 is subtracted from this total to account for the offender and their potential target. P is a randomly selected number between -2 and 2 that represents the offender's perception of the capability of the other citizens who are present. If G < 1, the offender determines that there are not enough capable guardians present, so they should commit a crime. If G == 1, the offender is unsure if there are capable guardians present, and so makes a random decision to commit the crime. And finally, if G > 1, the offender determines that there are capable guardians present and they should therefore not commit the crime.

Now, assume G <= 1 and the offender has decided to commit the crime. Which agent should the offender offend? The offender finds the wealthiest person in that node and robs that person.

In Groff's implementation, if S >= 0, the offender determines that the target is suitably wealthy and robs them. If S < 0, the offender determines that the target is not suitably wealthy, so they do not rob them. We decided that this check is unnecessary in the context of our experiment; according to Groff's implementation, there is a higher chance that an offender will rob another Citizen who is wealthier than them, but the same offender might actually rob other Citizens who are of equal or lesser wealth, as well, albeit with lower likelihood. As a result, we omitted S because we believe that in the long run, the number of crimes committed will not be different between a model in which offenders only rob Citizens wealthier than them (our model) and a model where offenders mainly rob wealthier Citizens, but have a chance of indiscriminately robbing other Citizens (Groff's model). Our modified version of Groff's decision tree is shown in Figure 1.2.

After running simulations using our model, we generate the following figures to show the spatial distribution of crimes committed. For reference, the figures Groff generates in her own experiment are also shown.

Figure 2.1. The distributions of crimes across Groff's model for varying randomization conditions.

Figure 2.2. The distributions of crimes across CrimeWorld for 100, 200, 300, 400, 500, and 600 steps.

Figures 2.1 and 2.2 display the spatial distribution of crimes committed across Seattle and CrimeWorld, respectively. In Figure 2.1, the distribution of crimes in Groff's model shows that there is an area of higher crimes committed that emerges where there is a bottleneck present in the map, and where the nodes are the most dense. This figure is generated using varying randomization conditions, which are based on the amount of time the agents in the model spend away from home (from 30% to 70%) to support Groff's investigation into routine activity theory. Figure 2.2 displays our model's results, which are not based on randomization conditions nor routine activity theory, but rather time steps. Similar to Figure 2.1, Figure 2.2 shows that there are dark areas of CrimeWorld where more crimes are committed, which darken as more time passes. These dark areas are close to clusters where Citizens live, since they return to their homes regularly.

For the purposes of measuring how closely our model matches Groff's, we also find the mean difference between the number of crimes committed for various conditions relating to how much time each Citizen spends away from their home. Figures 3.1 and 3.2 show Groff's results and our results, respectively.

Figure 3.1. A comparison of the average number of robberies per node for different percentages of time away from home in Groff's model.

Figure 3.2. A comparison of the average number of robberies per node for different percentages of time away from home in our model.

From Figure 3.2, we observe that the differences in the average numbers of robberies in CrimeWorld for varying times away from home quantitatively differ from that of Groff's implementation. This is likely due to the fact that her simulation takes into account the shape and neighborhoods of Seattle, and because Groff runs her simulations for a year's worth of time, whereas we run ours for about 30 days due to time limitations. Qualitatively, however, the differences in average number of robberies in Crimeworld follow the pattern of that in Groff's simulation; if we multiply each value we obtain by a factor between 3 and 5, we output values that are the same as Groff's. For example, for I=0.3 and J=0.4, the mean difference is -21.39 in Groff's experiment and -4.73 in ours. If we multiply our result by 4.52, however, our result matches Groff's. Similarly, for I=0.3 and J=0.5, the mean difference is -40.58 in Groff's experiment and -10.91 in ours. Again, if we multiply our result by 3.72, our result matches Groff's. We summarize the factoral differences between our results and Groff's in Figure 4.

Figure 4. Factoral differences between our results and Groff's results for the mean differences between the average numbers of robberies per node for different percentages of time away from home.

Our version of CrimeWorld, as implemented according to Groff's experiment, does not include punishment for committing crimes. In fact, when an offender decides whether to commit a crime in a node, they also consider whether there are any police agents in the node, and if so, the offender simply does not rob anyone, effectively avoiding punishment. We propose a version of CrimeWorld where offenders do get punished if they are caught committing crime. In this CrimeWorld full of punishment, we increase the motivation of offenders who commit crimes successfully and decrease the motivation of offenders who are caught while committing crimes.

When deterrence in the form of punishment is introduced to CrimeWorld, the number of crimes committed should decrease, since the purpose of punishment is to lower the number of crimes committed.² The factors that drive offenders to commit crimes outweigh the factors that deter them; successfully committing a crime and needing more wealth both contribute to an offender's motivation to commit crime, while only being caught lowers that motivation. Furthermore, people in a state where they cannot afford the necessary living expenses of their location any longer are more likely to turn to crime in order to improve their situations, since they have little left to lose.

In CrimeWorld 2.0, each Citizen starts out with different values for wealth and for income. As a result, we introduce economically diverse Citizens; there are some Citizens who have wealth but no income (potentially like real-world retirees), some Citizens who have income but no initial wealth (potentially like real-world immigrants with jobs), and some Citizens who have no wealth and no income (potentially like real-world homeless people), as well as others. We also implement a cost of living value, based on the cost of living in Seattle, which we calculate to be approximately $53,712 per year.⁴ Another major change we implement from our original model is that the police officers in CrimeWorld 2.0 are undercover, such that if a crime is committed while a police officer is in a given node, the Citizen(s) who commit a crime will be punished. We run our simulation for two different types of punishments; each offending Citizen pays either a set fine for every crime they are caught committing, or a fine that is proportional to how wealthy the Citizen is.

The decision tree an offender uses to decide whether to commit a crime under CrimeWorld 2.0's new environment is shown in Figure 6.

Figure 6. The offender's decision tree based on wealth in CrimeWorld 2.0.

With the introduction of punishment, we also implement motivation, the main mechanism that determines whether a Citizen commits a crime. Motivation increases depending on how little wealth a Citizen has and how many times a Citizen successfully commits crimes, and decreases depending on how many times a Citizen has been punished. These relationships are defined by the equation below, where M is motivation, S is the number of times a Citizen succeeds in committing crime, and C is the number of times a Citizen is caught committing crime.

When a robbery is committed, motivation is recalculated with this formula. The more successful an offender is in committing crimes, the less their motivation decreases when they are caught. If an offender is caught committing a crime, but the number of times they succeed exceeds the number of times they fail, their motivation is not recalculated, but instead, it decreases. If the offender is not caught committing a crime and the number of times they succeed does not exceed the number of times they fail, their motivation is still recalculated in order to take these values into account. Likewise, if an offender is not caught committing a crime but the number of their failures exceeds their successes, their motivation is not recalculated, but instead, it increases. If an offender is caught committing a crime and their successes exceeds their failures, their motivation is still recalculated to take these values into account.

Building off of the decision tree shown in Figure 6, Figure 7 shows the decision tree an offender uses to decide whether to commit a crime when motivation is introduced as a factor.

Figure 7. The offender's decision tree based on motivation in CrimeWorld 2.0.

After running simulations using our new model, we generate the following figures to show the number of crimes committed for differing values and proportions of punishment.

Figure 8.1. The number of crimes committed for varying values of punishment.

Figure 8.2. The number of crimes committed for varying proportions of punishment.

For Figure 8.1, we observe a downward trend in number of crimes that levels our at approximately 8063; however, at a punishment value of 70, there is an extreme spike in number of crimes. From this figure, we can see that at a punishment value of 100, the number of robberies reaches the minimum. Any punishment value more than 100 is never lower than 100. In Figure 8.2, we can see that there is a global maximum at a punishment ratio of 0.2 and a global minimum at a punishment ratio of 0.5. In comparing Figures 8.1 and 8.2, we can see that CrimeWorld 2.0 has the lowest amount of crime when the punishment fine is a half of the offender's wealth. Otherwise, CrimeWorld 2.0 should have a set punishment value of 100. The extreme spikes in both figures indicates that a fine should not be an arbitrary value but one that can be proven to be one that reduces the number of crimes the most.

There is room for several different extensions, which can improve the applicability of our experiment to the real world. For one, it might be an interesting experiment to analyze the number of Citizens who go into debt throughout the simulation because this may inspire some analysis of the effects on Citizens of the amount of punishment and their cost of living. The purpose of punishment is to lower the number of crimes offenders commit, and the cost of living in any city should be low enough that even a Citizen with a minimal income can get by. However, there must be a point where either the cost of living is too high, resulting in more Citizens falling into debt and therefore committing more crimes, or the cost of punishment is too high, resulting in more Citizens falling into debt and remaining in debt as the risk of committing a crime and getting caught is too high, or both.

In conclusion, we find that punishing offenders by removing half of their wealth is the most effective punishment in terms of lowering the total number of crimes committed. In the context of the real world, this is different from how punishment is allotted for real robberies; in Washington state, theft of the third degree is punishable by a $5,000 fine, increasing to $10,000 for the second degree and $20,000 for the first degree.¹ For some people, $20,000 is not a significant amount of money; it's only 2% of the wealth of a person with a million dollars. However, for someone with no wealth who only makes enough to cover the cost of living from year to year (approximately $53,712), it's almost 40% of the money they need to live comfortably. Should they not be able to make ends meet, there are several things this person can do to improve their situation, one of which is to turn to crime. Based on the results of our experiment, we believe that the best way to fairly punish all criminals, regardless of their wealth, is to remove a proportion of their wealth. We acknowledge that there are countless factors that we do not account for with our model, since the real world is much more complex than our model, but our results are consistent with the idea that punishment should be a proportional value, not a fixed value.

1. Baker, Lewis, Schwisow and Laws. (2014). A Guide to Theft Laws & Penalties in Washington State. Baker, Lewis Schwisow & Laws, PLLC.

A guide to the laws in Washington State regarding theft of the 1st, 2nd, and 3rd degrees.

2. Carlsmith, K. M., Darley, J. M., & Robinson, P. H. (2002). Why do we punish? Deterrence and just deserts as motives for punishment. Journal of Personality and Social Psychology, 83(2), 284-299.

It's a common theme in law that a person deserves punishment proportional to the crime that they commit, and therefore, punishing an offender reduces the frequency and likelihood of future offenses. The authors examine the incentives people have for committing crimes and the reasons that might deter them.

3. Cohen, Lawrence E., and Marcus Felson. "Social change and crime rate trends: A routine activity approach." American sociological review (1979): 588-608.

Cohen and Felson introduce the idea of routine activity theory in which they state that crime is not affected by social causes such as poverty or unemployment. They focus on the circumstances under which an individual carries out a crime. During their time, the conventional theories of crime was unable to explain why crime rates increased post World War II since the economy was on the rise. Their routine activity theory states that there was more crime post WWII since people were generally more wealthy and there was more to steal.

4. Cost of Living in Seattle, Washington, United States. (2017, December 10). Retrieved December 10, 2017, from https://www.expatistan.com/cost-of-living/seattle.

A table listing the living expenses a person might have if they live in Seattle, Washington. The total expenses are about $53,712 per year.

5. Groff, Elizabeth R. "Simulation for theory testing and experimentation: An example using routine activity theory and street robbery." Journal of Quantitative Criminology 23.2 (2007): 75-103.

This paper presents a new approach to testing the routine activity theory. The routine activity theory is a criminology subfield developed by Marcus Felson and Lawrence E. Cohen. Routine activity theory is based on the premise that crime is committed regardless of social causes such as poverty, inequality, and unemployment. Some crimes that are well modelled by routine activity theory is copyright infringement, peer-to-peer file sharing, corporate crime, etc. The author of this paper, Elizabeth R. Groff, uses agent-based modelling to model street robbery since it involves the interaction of agents in a public place and is driven by economic gain, making it more of a rational decision than a crime such as assault. A wide variety of studies from surveys of individuals to macro and micro level data to represent routine activity in society. However, all of these studies struggled with separating constructs and accurately replicating crime patterns. Rather than the usual top-down approach, agent-based modelling is a bottom up approach that starts with individuals with characteristics and behavioural rules already implemented. This model introduces a new framework for more complete and rigourous tests of theories. It clearly supports the possibility of the basic premise of routine activity theory.

6. Harrell, E., Ph.D., Langton, L., Ph.D., Berzofsky, M., Dr.P.H., Couzens, L., and Smiley-McDonald, H., Ph.D. (2014, November 18). Household Poverty and Nonfatal Violent Victimization. Retrieved December 09, 2017, from https://www.bjs.gov/index.cfm?ty=pbdetail&iid=5137.

Presents findings from 2008 to 2012 on the relationship between households that were above or below the federal poverty level and nonfatal violent victimization. For the period 2008–12: Persons in poor households at or below the Federal Poverty Level (FPL) (39.8 per 1,000) had more than double the rate of violent victimization as persons in high-income households (16.9 per 1,000). Persons in poor households had a higher rate of violence involving a firearm (3.5 per 1,000) compared to persons above the FPL (0.8–2.5 per 1,000). The overall pattern of poor persons having the highest rates of violent victimization was consistent for both whites and blacks.

7. Malleson, Nick, Heppenstall, Alison, and See, Linda. "Crime reduction through simulation: An agent-based model of burglary". Computers, Environment and Urban Systems Volume 34, Issue 3 (2010): 236-250.

Malleson et. al. introduce a model in which they simulate burglaries that happen within an environment where the burglars' need to acquire wealth fluctuates with their need to sleep (so it decreases when they are tired and increases after they sleep). The authors find that burglary rates increase in certain areas in their model, leading them to suspect that if these areas had increased security, the rates of burglaries would decrease. Altering the security in different environments produces different burglary rates and community types within 50 days (according to the simulation's timeline). We think that this article would provide an interesting basis for an extension to Groff's experiment, in which we might implement exhaustion as a property of crime-committing agents and simulate areas with higher or lower security to observe how these agents behave under varying circumstances.

8. Sackett, C. (2016, June). Neighborhoods and Violent Crime. Retrieved December 09, 2017, from https://www.huduser.gov/portal/periodicals/em/summer16/highlight2.html.

This extensive report investigates the various causes of violent crime in the US. Violent crime rates have decreased in recent years, but remained stagnant or even increased in select neighborhoods. This could be due to a variety of factors, such as housing, inclusion, and access to public safety. There are some ways to reduce this violent crime, the most prominent of which is giving opportunities to youths living in these neighborhoods.

9. Visher CA, Roth JA (1986) Participation in criminal careers. In: Blumstein A, Cohen J, Roth JA, Visher CA (eds) Criminal careers and "Career Criminals", Vol I. National Academy Press, Washington DC, pp 211–291.

An article cited by Groff⁵ regarding developing effective crime control policies.