Transcription
If you have issues viewing or accessing this file contact us at NCJRS.gov.,oo(?60'!\,o'0(}}'l0.: 0.I'.1 ,o p"-i)L'0"o,vI:)c'c,. .A Di1 IIC.(j) HODEL FOR DISCRIMTNATIONoBETif'iEN INCAPACITATION D DETERRENCE.'\\by:'o-.' ! ,"Charl s J. Malmborg,J .'.iandStuart Jay De'tLt,sch'"(( I,) \,I':1i),0,0 School ,9 Industrial and SY,stemsli Engineeringo \(;eorgfli' In'StituteofTechnology,, t)1.anta, Georgia' 30J32Marc.h, 1978(\,)\\( ':.1o iJ(/,-;;'.11 -- -::::: c-::;'::::::- ::;-t:::-T)", t.'0,",-;;.Q(I
A DYNANIC NODEL FOR DISCRININATIONBETlillEN INCAPACITATION ANDDETE}L ENCEbyCharles J. Malmborg andStuarc Jay DeutschNCJRSAUG 2'\. \979fo.CQU\SlTlONS School of Industrial ar.d Systems EngineeringGeorgia Institute of TechnologyAt anta, Georgia30332March, 1978
-----.------------------------------------- ii ACKNOWLEDGENENTSThis work was performed under Grant No. 75 NI-99009l, from the National Institute of Law Enforcement and Criminal Justice.Pointsof view or opinions stated in this document a.re those of the authorsand do not necessarily represent the official position or policies of the United States Department of Justice.The substance of this work also served as [34] a }faster ofScience l esisby C. lmborg.
iii TABLE OF CONTENTS ACKNOWLEDGEMENTSPagei1LIST OF TABLES .viiLIST OF ILLUSTRATIONS.ixSUMMARY.xiChapter t.I.1.11.2II.2.22.32. Lt·2.52.6III. 236Crime in Society.2.1.1 Measurement of the Crime78P teDeterrence. . .Incapaci"tation. . . . . . . .Basic Methods in Crime Rate Modeling for StaticSystems. . . . . Research Objectives.Overview of the Research2.4.12.4.22.4.32.4.42.4.5 1".I.ITEFATURE SURVEY 2.1 .INTRODUCTION. .9130Offender Behavior Hode1ing . .Conviction Probability Modeling Ag*regate Offense Hode1ing . Nt Time Out Models . . . .Current Work in Crime Rate Hode1ing . 151617202222Basic Methods for Nonstationary Systems. 2.5.1 Stochastic Empirical Models . . 2.5.2 Dynamic Modeling of the Criminal Population.2.5.3 Fluctuations in Crimina.1 Population as aMarkov Proces 2533Summary . 342830MODEL DESCRIPTION . 353.13.23.3354042Form" of the Model Specification of Z . . .Specification of Kt.
ivChapterPage3.3.1III.3.3.2 3.3.33.3.43.43.5 3.6 IV.Des ription54575859········· ·······Comparison of Hodels.Summary.HODEL EXECUTION4.14.2 mmary of the Primary Model and �·················· ·3.3.6··Specification of A·Specification of D · · · ·······3.5.1 The Deterrent Formulation3.5.2of the Policy Space·3.3.5 Motivation for Using Time Series Modelingof PtApplication of the Blumstein, Nagin andCohen Hodel'.Blumstein's Three-Way Partitioning.Blumstein's Three-Way Hodel as a MarkovProcessDiscussion of Flow Variables in the MarkovProcessClosed Form Transient Results·60·······, ····.····061···65·····66Utilizing the Offenses Modeling Technique of DeutschExecuting Blumstein's Criminal Population Model.4.2.1 Recidivism in Blumstein's Criminal PopulationModell 2. 2 Simulation of the Harkov Chain UnderlyingBlumstein's Model.'4.2.2.1 The Iterative Procedure forExecuting the Markov Chain[,.2.2.2 Computation of Kt.················ ······· ·· ··············69 4.3 4.4 ·.······Using the Model.5.1.1 The Structure of d(Q,S)7172747575767677787980COMPUTATIONAL EXPERIENCE.5.1 Utilization of Nagin's Deterrence Formulation.4.3.1 Solution for Dt4.3.2 Solution for Prevailing Q and S4.3.3 The Optimization Procedure.4.3.3.1 Solution for Yo Values4.3.3.2 Solution for Yl and Y2 Values.4.3.4 Formulating the Optimization to DetermineQ* and S*Summary.68690 4782···············8283
.'., v PageChapterv5.1. 2Notivation for the Necessary Assumptionsto Solve Yi .5.1. 3 Determination of Yo 5.1. 4 Determination of Yl and Y2' . . 5.1.5 Solution for the Optimal Policy 5.1. 6 Limiting Cases of Q and S . .5.1.6.1 The Case of Zero Sanctions5.1. 6.2 The Case of Infinite Sanctions .5.1. 7 Sensitivity of the Model to the NecessaryAssumptions . . .5.1. 8 The Implications of the S Assumption.5.1. 9 The Implications of the Assumption, - -:.'-"' --5.2 5.3 8888909093Analysis Using Georgia Data. .5.2.1 Input Policy Variables for Georgia. .5.2.2 Total Reported Offenses in Georgia. . . .5.2.3 Prison Populations in Georgia 5.2.4 Criminal Population Hovement in Georgia5.2.5 Behavior of At in Georgia . . . . .5.2.6 General Deterrent Effects in Georgia.5.2.7 Optimization Process for the GeorgiaData Base . . . . . . 5.2.8 Motivation for Using Constant InputPolicy Variables. . . . . .5.2.9 Evaluation of the Impact of Optimization. 5.2.10 Discussion of Sample Results . ,. . .101102The Effects of Nonstationary and/or CorrelatedSentencing Practices . . 5.3.1 Average Sentence Length . .5.3.2 Probability of Imprisonment GivenConviction. . 11111195969698991021051061071135.4Sensitivity Studies in the QsS Policy Space. 1185.4.1 Design of a Factorial Experiment. . .1205.4.2 Analysis of Experimental Results. . 1235.4.3 Analysis of Linear Results. . 1275.4.4 Experimentation Within Plausible Limits ofCurrent Corrections Capacity. . 1345.4.5 Comparison of Results Between Models. .1375.4.5.1 An Illustrative Example. 1375.4.5.2 Example Discussion. 1385.4.6 Development of a Q-S Nomogram. 1395.5Separating Incapacitation from General Deterrence.5.5.1 Formulation of the Incapadtative Effect. 5.5.2 Simulation of the Incapacitative Effect5.5.3 The Effect of Optimizat·ion.5.5.4 Comparison Between Hodels . . 8484858787139141142145147
viChaptervPage5.6 VICONCLUS IONS6.16.2 Introduction to the Comparison Procedure5.6.1 Input Requirements . . . . . . .5.6.2 Total Offenses for Missouri . .5.6.3 Total Reported Offenses in Texas . .5.6.4 Missouri Prison Populations5.6.5 Texas Prison Populations . 5.6.6 Nissouri Prison Admissions.5.6.7 Texas Prison Admissions . 5.6.8 Average Sentence Lengths in Missouri.5.6.9 Average Sentence Lengths in Texas . .5.6.10 Probability of Imprisonment for Hissouri. .5.6.11 Probability of Imprisonment for Texas5.6.12 Discussion of Corrections Capacity i Texasand Missouri. . . . , 5.6.13 Results of Model Simulation for the Texasand Missouri Data Bases . . 5.6.13.1 Results of Model Simulation forthe Texas and Missouri Data Bases5.6.13.2 Deterrent Eff cts in Texas andMissouri. .5.6.13.3 Comparison of the Effect ofOptimization.5.6.13.4 Comparison of Savings ThroughOptimization. . . .5.6.13,5 Separating Incapacitation fromDeterrence. .A -nRECOMHENDATIONS Conclusions . . 165169170170170172175177177180APPENDIX . 182BIBLIOGRAPHY 212
vii LIST OF TABLES Table1.Plausible Bounds on Flow Parameters . 512.Partial List of Comparative Attributes. 633.Total Reported Offenses for Georgia 974.Total Reported Offenses Forecasted for Seven Periods.985.Georgia State Institution Inmate Population Totals. 996.Illustration of Growth in Georgia State Prison Populations. 1007.Criminal and Prison Population Percentages. .8.Sample Results for Seven Periods.1029.y. Values for Seven Periods . 10310.Optimization Results for Georgia. 10511.Eh ected12.Aver age Sentence Lengths in Georgia13.Honthly Probability of Imprisonment for Georgia 11414.Optimization Results for the Nine Starting Points · 12215.Percentage Changes in Q12416.Percentage Changes in S12517.Summary of Responses in ANOVA Format. 18.-Preliminary ANOVA 19.Final ANOVA 20.Model Comparison Summary.· 101 . Total Offenses in Georgia. 00 0 108 113 131131 132 138
'. viii21.Honthly Georgia State Prison Receptions . 14422.Percentage of Overall Effect of Sanctions Q and S Due toIncapacitation for Policy: Q .306, S 1.67 Years. 146Percentage of Overall Effect of Sanctions Q and S Due toIncapacitation for Policy: Q .4605, S 1.11 Years. 14623.24.Percentage Savings Due to Incapacitation.25.Total Reported Offenses in Nissouri 15126.Total Reported Offenses in Texas. . 15227.Missouri Prison Populations . 15428.Texas Prison Populations . 15529.Missouri Frison Admissions. .· 15831.Average Sentence Lengths for Hissouri32.Average Sentence Lengths for Texas. 1.6433.Imprisomnent Probabilities in NissourL16634.Impr,isonment Probabilities in Texas16735.At For Five Sample Periods. .36.Ct/Ct P37.Deterrent Effects For Five Sample Periods 38.Summary of the Optimization Process For Q and S 39.Crime Saving Percentages. l7l 40.Distribution of Crime Control Effects176tRatio For Five Sample. Peri.ods.148 161. . . 171· . . . 171· 172 173
ix LIST OF ,e 1.The Criminal Justice System . . . 362.Summary of the Logical Relationship .383.Summary of Hodel Components in Relation to the ThreeBuilding Blocks . . . .394.Blumstein's Descriptive Hodel of Society.465.The Macro Flow Diagram. 676.Transition }Iatrix Underlyirlg the }'.arkov Chain .707.Procedure for Executing the Markov Process.718.Figurative Summary of the Search Process.739.Flow Diagram Summary of D Analysis t7510.The Behavior Distribution . . . 10911.Average Sentence Length Time Seri(:s of Georgia. . . 11212.Probability of Imprisonment Time Series for Georgia13.Behavior of Forecasted Q Values 14.Starting Points For the Factorial Experiment. 12115.Percentage Change Plot of Q 12616.Percentage Change Plot of S17.Graphical Test of Linear Assumption in Q.18.Graphical Test of Linear Assumption in S.19.Q* vs. QxS 20.Q*-S* Nomogram for Incremental Changes in CorrectionsExpenditure ILLUST TIONS0 0 ellS117126 0. .c130 136 129 c140
'. x21-Monthly Prison Receptions Time Series22.Total Reported Offenses Time Series23.Prison Populations Time Series.24.Prison Receptions Time Series25.Average Sentence Length Time Series26.Imprisonment Probability Time Series.143.'.· 150··156159163.168
xi SUNNARYA model is presented which simulates the criminal justicesystem over a 25 year horizon. The simulation is run over discreteqne month periods incorporating the court, corrections and lawenforcement systems.The model is used to determine the effect ofvarious sentencing strategies involving tne certa:i.nty and severity of punishment.Those sentencepolicie which correspond to thegreatest est,imatec crime control effect are identified as optimalsolutions.Extensions of the analysis are developed to specify theincapacitative and deterrent effects embodied in prevailing andoptimal solutions.10 addition, results of the model aJ:e presentedfor data bases originating in different geographica.l areas and a detailed comparison is performed.r.i ally.methods for the validationof the model are presented and validation results a.re outlined.
1 CHAPTER I INTRODUCTIONThe alarming rise in the level of crime experienced by oursociety in the past decade indicates a definite need forthe criminal justice system. re examiningFrom 1965 to 1976, the crime rate in theUnited States rose by over 140%.Although the theories explaining thisincrease are varied, most experts will agree that growth of the absolutelevel of deviance in society stems mainly from a breakdown in the committment to conformity on an individual level.The impressivemagnitude of this breakdown has led many researchers to believe thatthe individual's decision to engage in illegal activities is a function of his perception of the economic costs and rewards for doing so incombination with the criminal's idiosyncratic utility structure.In the earliest years of the rapidly growing crime rate, the popular strategy for dealing with the problem was to try and modify thebehaviors and character of the individual during incarceration.Thistrend led to a large increase in expenditures for experimental programs such as training and work therapy centers within correctionalinstitutions.Perhaps, due to its outwardly rehabilitative appearance,this approach for dealing with offenders held great popular appeal for many until about 1974.literature appeared which presented evidence showing the failure ofrehabilitation. Around that time, a significant body ofMost such studies showed recidivism rates for
2correctional institutior.s to be roughly the same whether or notrehabilitative programs were present. As a result, the emphasis, atleast in the research area of criminal justice, changed to moreobjective resource management problems within the system.Much of the analytical research from 1975 to the present, in the area of resource constrained crime rate modeling, has addressed thequestion of allocation for a fixed resource rather than the absolutelevel of that allocation. In addition, concentration has switched fromattacking the problem on an individual level to viewing the system inthe aggregate.Here, judicial policy is seen as the controllablevariables as opposed to "in-house" corrections policy. attention has been directed toward determining what judicial policywithin a stated expenditure level is associated with the lowestpossible crime rate. Specifically,A judicial policy consists of some trade-offcombination of the certainty of imprisonment and the length ofimprisonment meted out to convicted criminals.Most of the research addressing this question up until now has been unable to distingl1.ish between the effects of these two variablesin quantitative terms.This has made it a difficult task to clarifythe nature of "optimal" solutions. In addition, recent modeling hasbeen static in nature and unable to account for changes in eitherindogenous and exogenous variables including time.1.1Research ObjectivesThe objective of this research is to extend the approach takenin previous research to circumvent some of the shortcomings mentioned
3in the previous section.In particular, a dynamic mod
Figurative Summary of the Search Process. Flow Diagram Summary of D t Analysis The Behavior Distribution . . . ix 36 38 39 46 67 70 71 73 75 . 109 11. Average Sentence Length Time Seri(:s of Georgia. . . 112 12. Probability of Imprisonment Time Series for Georgia ellS 13. Behavior of Forecasted Q Values 117 14 .
