Transcript Arrest Rate, Crime Incidents, and Enforcement

Optimal Police Enforcement Allocation
Rajan Batta
Christopher Rump
Shoou-Jiun Wang
This research is supported by Grant No. 98-IJ-CX-K008 awarded by the National Institute of Justice,
Office of Justice Programs, U.S. Department of Justice. Points of view in this document are those of the
authors and do not necessarily represent the official position or policies of the U.S. Department of Justice.
UCGIS, Feb 2000
Motivation
“Our goals are to reduce and prevent crime,…
and to direct our limited resources where
they can do the most good.”
- U.S. Attorney General Janet Reno
- Crime Mapping Research Conference, Dec. 1998
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Consider Crimes Motivated
by an Economic Incentive
Auto theft
Robbery
Burglary
Narcotics
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Literature Review
 Cornish et al. (Criminology, 1987):
Criminals seek benefit from their criminal behavior.
 Freeman et al. (J. of Urban Economics, 1996):
A neighborhood with higher expected monetary return is
more attractive to criminals.
 Greenwood et al. (The Criminal Investigation
Process, 1977): A neighborhood with lesser arrest
ability has a larger amount of crimes.
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Literature Review
 Caulkins (Operations Research, 1993):
Drug dealers’ risk from crackdown enforcement is
proportional to “total enforcement per dealer
raised to an appropriate power”.
 Gabor (Canadian J. of Criminology, 1990):
A burglary prevention program may decrease local
burglary rates, but increase neighboring rates geographic displacement.
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Arrest Rate (PA), Enforcement (E)
& Crime Incidents (n)
 PA(E,n) = 1- exp(-E/n)
 = arrest ability value
(Caulkins)
Crime Level
 Under constant E,
PA decreases in n
(Greenwood et al.)
 PA increases in E
 Effect of E is more
significant for small n
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Monetary Return (R), Wealth (w)
& Crime Incidents (n)
 R(w,n) = c w exp(-n)
c,  depend on crime type
Crime Level
 R decreases in n
 Physical Explanations:
Limited by the wealth
of the neighborhood
Victims become aware
and add security
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Expected Monetary Return (E[R])
& Crime Incidents (n)
 E[R]= R(w,n)*(1-PA(E,n))
=c w exp(-E/n-n)
(Freeman)
Crime Level
 For small n, E[R] is small
because of high arrest
probability.
 For large n, E[R] is small
due to many incidents.
 E forces the E[R] down.
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Crime Rate & Socio-Economy
 One area is relatively crime-
free (Amherst)
 Another area is relatively
crime-ridden (Buffalo)
 Expected return for crime,
E[R], may equally attract
offenders
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Crime Equilibrium
 At equilibrium, number of
crimes is either 0 or n(2)
Opportunity
Cost of crime
m
E[R]
If n<n(1), high arrest rate;
all criminals will leave
If n(1)<n<n(2), return>cost;
attracts more criminals
If n>n(2), over-saturated;
some criminals will leave
n(1)
n*
n(2)
 n*: organized crime
equilibrium
Crime Level
UCGIS, Feb 2000
Crime Crackdown
m
Opportunity
Cost of crime
 Sufficient enforcement, E,
can lower expected return
curve E[R]
E[R]
E
 If E[R] curve < m, there is
no incentive for criminals;
crime collapses to 0
Crime Level
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Minimizing Total Crime
(2 Neighborhoods)
 Objective 1: Minimize total number of crimes
 Optimal Allocation Policy:
one-neighborhood crackdown policy is
optimal: place as many resources as necessary into
one neighborhood; if resources remain, into the other.
Generally, the neighborhood with better arrest ability
tends to have higher priority to receive resources.
Under equal arrest ability: affluent neighborhood has
priority only if both neighborhoods can be collapsed.
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Minimizing Crime Disparity
(2 Neighborhoods)
 Objective 2: Minimize the difference of crime numbers
 Optimal Allocation Policy:
The difference of the crime numbers can be minimized
to 0 unless the wealth disparity between them is large.
Under equal wealth, allocation of resources is
inversely proportional to arrest ability.
If the wealth disparity between the two
neighborhoods is large, the affluent neighborhood has
priority.
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A Numerical Example
 Data:
Arrest ability: 1 = .35, 2 = .10
Wealth level: w1= $30,000, w2 = $25,000
 = .02; c = .01; m = $15.
 Calculated Values:
Enforcement required to collapse crimes in NB1=320 hours
Enforcement required to collapse crimes in NB2=990 hours
Note: Every day, Buffalo Police Department patrols 300-500
hrs in each of its five districts and the number of call-forservice in each district is about 100-150.
 Decision Variable: x (proportion of enforcement allocated in NB 1).
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Total Enforcement = 1000 hours
x = .01
x = .265
x = .3
x = .32
n1 = 149; n2 = 0
n1 = 106; n2 =106
n1 = 94; n2 = 108
n1 = 0; n2 = 110
Total = 149
Total = 212
Total = 202
Total = 110
Difference = 149
Difference = 0
Difference = 15
Difference = 110
(dominated)
(non-dominated)
------- Neighborhood 1; ------- Neighborhood 2
UCGIS, Feb 2000
Total Enforcement = 520 hours
x=0
x = .32
x = 0.5
x = 0.62
n1 = 150; n2 = 119
n1 = 127; n2 = 127
n1 = 107; n2 = 131
n1 = 0; n2 = 133
Total = 269
Total = 254
Total = 238
Total = 133
Difference = 31
Difference = 0
Difference = 23
Difference = 133
(dominated)
(non-dominated)
------- Neighborhood 1; ------- Neighborhood 2
UCGIS, Feb 2000
Total Enforcement = 300 hours
x=0
x = 0.4
x = 0.5
x=1
n1 = 150; n2 = 129
n1 = 134; n2 = 134
n1 = 130; n2 = 135
n1 = 94; n2 = 141
Total = 279
Total = 268
Total = 265
Total = 235
Difference = 21
Difference = 0
Difference = 5
Difference = 47
(dominated)
(non-dominated)
------- Neighborhood 1; ------- Neighborhood 2
UCGIS, Feb 2000
Optimal Enforcement Allocation
(Multiple Neighborhoods)
 Objective 1: Minimize total number of crimes
The neighborhoods should be either cracked down or
given no resources except for one of them.
The neighborhoods with higher arrest/wealth value
have higher priority.
 Objective 2: Minimize the difference of crime numbers
“Evenly” distribute enforcement to the wealthier
neighborhoods such that the wealthier neighborhoods
have the same number of crimes.
UCGIS, Feb 2000
BPD Case Study
Buffalo Police Department
 ~42 Square Miles
 5 Command Districts
 ~6700 calls for service/wk
 ~6400 patrol hours/week
 ~530 police officers
 30-55 patrol cars at any
time w/ 2 officers/car
UCGIS, Feb 2000
Burglary Data in Buffalo
District
Median Household
Weekly Patrol
Total Burglary
Arrest Prob.
Income (w)
Hours (E)
Numbers (n)
(PA)
A
$21,250
896.0
187
13.37 %
B
$13,750
1485.4
350
23.86 %
C
$13,750
1536.0
481
13.72 %
D
$21,250
1314.1
373
9.65 %
E
$21,250
1183.3
304
16.78 %
6414.8
1695
15.43%
Total
UCGIS, Feb 2000
Minimizing Burglary Disparity in Buffalo
Arrest
Opportunity
Optimal
Required Hours
Number of
Ability
Cost
Patrol Hours
to Collapse
Burglaries
()
(m)
(E*)
Crime Activity
(n*)
A
.0300
157.0
252.1 (3.9%)
2967.6
329
B
.0612
79.0
1475.8 (23.0%)
2663.3
329
C
.0462
79.0
1954.9 (30.5%)
3528.0
329
D
.0288
138.5
1696.7 (26.5%)
4371.7
329
E
.0472
138.5
1035.3 (16.1%)
2667.5
329
6414.8 (100%)
16198.1
1645
District
Total
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Current and Future Work
Geographic Information System (GIS)
implementation for crime mapping & prediction
Dynamic (iterative) model of crime displacement
Optimizing transportation model (Deutsch) of
geographic criminal displacement
Scheduling of BPD Flex Force
UCGIS, Feb 2000