Inter-Racial Crime Analysis
Today my post is unusual and out of schedule. It was inspired (or provoked) by various interpretations of inter-racial crime data presented in Andrew Sullivan post The Intermission Is Over [1]. Opposite conclusions were drawn from the same data by Elon Musk, Aaron Rupar, Eric Cartman, and Kareem Carr. I decided to apply pure math and made no a priori assumptions about results, and only self-evident mathematical model assumptions. I shared my thoughts with Andrew Sullivan first. Now I present them here.
Crime statistics can be dissected many ways to derive regularities and dependencies. For crime is committed between distinct racial, ethnic, gender, social, economic or other groups, the ability to reveal the nature of this crime, its regularities, and possible causes can lead to relevant policy changes. This paper presents a simple model and method for the analysis of crime committed between any distinct racial, ethnic, gender, social, economic or other groups. This model is applied for inter-racial crime data of 2018 in the USA. It is demonstrated that racism plays minor role in inter-racial crime. The geographical proximity is the main factor.
1. Model
In general, the number of person-against-person crimes is proportional to the number of the potential criminals times the number of potential victims. Hence, in a country it is proportional to the square of the total population. Following the same logic, the number of inter-group crimes must be proportional to the population of the perpetrator's group multiplied by the population of the victim's group. The general theory dealing with diverse populations must not be based on a scalar proportionality factor a, but on a tensor a(i,j):
C(i,j) = a(i,j) P(i) P(j), where i,j = W,B,H (1)
Here C(i,j) is the number of inter- and intra-racial violent crimes, P(i) and P(j) are the relative group population in the country.
This model takes into consideration the mathematical probability of meeting between individuals of different races by including relative racial populations for the entire country. The proportionality coefficient a(i,j) must depend on the local density of the population. Higher density increases probability of meeting another individual – a necessary condition for interpersonal crime to occur. So, in the city of two million there must be more crime than in the state of two million. The values of coefficients a(i,j) will be derived from the analysis of the inter-group crime statistics. In turn, analysis of these inter-group crime coefficients may reveal the trends and even the dominant causes of inter-group crime.
I will demonstrate the usefulness of this model by applying it to US Department of Justice violent inter-racial crime statistics for 2018 [2] (Table 1):
Victim
Perpetrator W B H
W 2.2M 0.06M 0.21M
B 0.55M 0.39M 0.11M
H 0.36M 0.04M 0.33M
Here W, B and H are the White, Black and Hispanic/Latino racial/ethnic groups. Right column indicates Perpetrator race, and top row indicates victim race.
The left column is the race of the perpetrator and the top row is the victims; e.g., we can see from this table that there are 60,000 acts of violence per year (2018) by Whites against Blacks, 210,000 acts against Hispanics, and 2.2 million against Whites.
2. Model application
Let us apply the proposed model on the statistics presented in Table 1. The relative racial population in the country: P(W)=59%, P(B)=13%, P(H)=19%. Combining the populations and numbers from Table 1, we can calculate the proportionality coefficients a(i,j). Here they are presented in tabular format (Table 2):
W B H
W 19.2 2.4 5.7 /1000
B 21.7 69.9 13.5 /1000
H 9.7 4.9 27.7 /1000
In a race-blind, homogeneously geographically distributed society all coefficients in this table would be equal. But they are not. One of the reasons is that the races are not homogeneously distributed. The neighbors of a White person are more likely to be White and the neighbors of a Black person more likely to be Black than within a homogenous distribution. Geographical proximity must have a considerable impact on the inter-personal crime – it’s more likely that crime will be committed against a person who lives in the neighborhood. One would therefore expect a higher percentage of intra-racial crime than in a geographically homogeneous multiracial society. The diagonal line in the table is the coefficients for intra-racial crime, and certainly, the diagonal coefficients are the highest. This just confirms that geographical proximity is the major factor.
Other coefficients are telling statistics on race relations and propensity for violent crime. Summing each row gives the probability of committing a violent crime by a member of a racial group per year (2018): W=0.0273, B=0.1051, H=0.0423. Summing the columns gives the probability of committing a violent crime against a member of a racial group per year (2018): W=0.0506, B=0.0772, H=0.0469. A White is twice as likely to be a victim than a perpetrator, a Black is more likely to be a perpetrator than a victim, and a Hispanic is roughly equally likely to be a victim or perpetrator. Note that Blacks and Hispanics are more likely than Whites to live in high density areas – cities, not suburbs or countryside. The above results confirm our assumption that propensity for interpersonal crime is a strong function of population density.
3. Diagonal Re-Normalization
Comparing inter-racial coefficients between White and Black and Black and Hispanic we see that a(B,W) is nine times larger than a(W,B), and a(B,H) almost three times larger than a(H,B). Does it mean that Blacks are more racist than Whites? That would be a premature conclusion. Blacks, as evident from Table 1, commit more violent offences than others. Majority of their victims are Black. If we re-normalize Table 2 to intra-racial crimes - dividing the numbers in each row by the intra-racial coefficient for that row - we can reveal the racism factor, i.e., how much the other inter-racial coefficients differ from 1 (Table 3 normalized to intra-racial crimes):
W B H
W 1 0.125 0.3
B 0.31 1 0.19
H 0.35 0.18 1
The sum of only the inter-racial coefficients of W (White perpetrators – top row) is 0.425, B (Black perpetrators – mid row) is 0.5 and H (Hispanic perpetrators – bottom row) is 0.53. All these numbers are of the same order of magnitude, suggesting that racism plays a minor role in inter-racial crime, while, geographical proximity plays the key role. The proportionality tensor a(i,j) is a strong function of population density.
4. Conclusion
In conclusion, I proposed a simple tensor model and method for statistical analysis of the inter-group crime data. Method consists of calculating the proportionality tensor and diagonal re-normalization. We applied this model on the US inter-racial violent crime data of 2018 and derived several characteristics of inter-racial crime.
One of the conclusions is the racism (or more exactly racial hatred) does not play important role in inter-racial crime, but geographical proximity does.
The local density of population is an important factor in interpersonal crime. More research must be done to derive the mathematical relationship between the rate of interpersonal crime and local population density.
References:
1.
