《LEGAL POLICY ANALYSIS FINDING AN OPTIMUM LEVEL OR MIX》

Part Ⅰ Finding an Optimum Level1

Chapter 1 The Policy Problem of Doing Too Much or Too Little： Pretrial Release as a Case in Point9

Ⅰ.The Problems and the Data9

A.The Basic Problems to Resolve9

B.The Data to Work With10

Ⅱ.A Causal Model Showing the Effects of Increasing the Percentage of Defendants Held15

A.The Basic Causal Model15

B.Compared to Alternative Causal Mod-els19

Ⅲ.Finding an Optimum Percent of Defen-dants to Hold Pending Trial23

A.With Linear Relations among the Variables24

B.With Nonlinear Relations among the Variables25

C.The Bottom Point on the Total-Cost Curve27

Ⅳ.A Causal Model Showing the Effects of Cost Changes on the Optimum Percent to Hold29

A.Determining the Direction of the Ef-fects30

B.Determining the Magnitude of the Ef-fects32

C.Diagramming, Summarizing, and Indi-vidualizing the Model34

Ⅴ.Further Policy, Causal, and Methodolog-ical Implications37

A.The Optimum versus the Empirical38

B.Expanded Causal Model with Further Policy Implications43

C.Expanded Applications to Other Poli-cy Problems46

Appendix 1A.Glossary of Terms67

Appendix 1B.Basic Formulas Used71

Chapter 2 Using Deductive Modeling to Determine an Opti-mum Jury Size and Fraction Required to Convict75

Ⅰ.The Basic Problems to Resolve75

A.Inability of Empirical Data to Indi-cate Effects of Jury Size75

B.Deductive Analysis to Indicate Ef-fects of Jury Size78

Ⅱ.The Basic Data to Use79

A.The Probability of Convicting an Average Defendant79

B.The Probability of Convicting an In-nocent or a Guilty Defendant81

C.The Number of Innocent and Guilty Defendants per 100 Defendants82

D.Summary and Consistency of the Ba-sic Data84

Ⅲ.Optimizing Jury Size85

A.Effects of Changes in Jury Size on Jury Errors85

B.The Optimum Jury Size When Con-victions of the Innocent Are Consid-ered 10 Times as Undesirable as Nonconvictions of the Guilty88

Ⅳ.Optimizing the Fraction Required to Convict90

A.Effects of Changes in the Fraction Required to Convict on Jury Errors90

B.The Optimum Fraction Required to Convict with a Trade-Off Weight of 1093

Ⅴ.Effects of Changing the Normative and Empirical Premises95

A.Effects of Changing the Normative Premises on the Optimum Unanimous Jury Size95

B.Effects of Changing the Empirical Premises on the Optimum Unanimous Jury Size99

C.Effects of Changing the Premises on the Optimum Nonunanimous Fraction Required to Convict103

Ⅵ.The Independent-Probability Perspective versus the Collective-Mind Perspective105

A.Calculating Conviction Probabilities Using an Unweighted Average for the Two Perspectives106

B.Calculating Conviction Probabilities Using a Weighted Average for the Two Perspectives107

C.Revised Data and Results110

Ⅶ.Variations on the Basic Model115

A.Effect of Jury Size on Representa-tiveness that Affects Conviction Probabilities115

B.Other Variations118

Ⅷ.Conclusions126

Appendix 2A.Glossary of Terms151

Appendix 2B.Basic Formulas Used155

Appendix 2C.The Impact of Jury Size on the Probability of Conviction157

Part Ⅱ Finding an Optimum Mix among Competing Policies159

Chapter 3 Developing an Optimum-Mix Strategy for Civil Rights or Other Multipolicy Activities163

Ⅰ.Basic Ideas163

A.The General Purposes and the Data163

B.The Substantive Problem and the Ba-sic Methodology164

Ⅱ.Scoring the Cities and the Activities165

Ⅲ.Finding an Optimum Mix between Two Civil Rights Activities171

A.Equal-Benefit Lines171

B.Optimum Allocation Points within Constraints172

C.Other Two-Activity Allocation Prob-lems176

Ⅳ.Finding an Optimum Mix among Six Civ-il Rights Activities177

A.Reading the Multiple-Activity Graph177

B.Finding the Optimum Allocations180

Ⅴ.The Substantive Meaning of the Correla-tion and Regression Coefficients183

A.The Role of Outside Variables like Region183

B.Negative Regression Coefficients and Causal Models187

Ⅵ.Input-Output Analysis Applied to Civil Rights Activities189

A.Working with a Variance-Accounted-for Matrix190

B.Working with a Regression-Coeffi-cients Matrix195

Ⅶ.Some Conclusions198

Appendix 3A.The Racial Discrimination Ques-tionnaire and the Average Response to Each Item209

Appendix 3B.Cities Used in the Analysis217

Appendix 3C.Glossary of Terms219

Appendix 3D.Basic Formulas Used223

Chapter 4 Finding an Optimum Geographical Allocation for Anticrime Dollars and Other Governmental Expenditures225

Ⅰ.Basic Ideas225

A.Goal to Optimize225

B.General Allocation Procedures226

Ⅱ.Allocation When Linear or Constant Re-lations Exist between Dollars Spent and Crimes Reduced228

A.With Data for Two Time-Points for Each Place228

B.With Data for One Time-Point for Each Place232

C.With Data for Three or More Time-Points for Each Place234

Ⅲ.Allocating When Nonlinear or Diminish-ing Relations Exist between Dollars Spent and Crimes Reduced237

A.With Data for Two Time-Points for Each Place238

B.With Data for One Time-Point for Each Place242

C.With Data for Three or More Time-Points for Each Place243

Ⅳ.Controlling for Demographic, Socioeco-nomic, and Other Variables245

A.The New Goal Variable of Reducing Crimes Not Explained by Demogra-phy245

B.The Use of the New Goal Variable to Calculate Linear and Nonlinear Slopes and to Reduce Positive Slopes247

Ⅴ.Comparing Geographical Allocation with Activity and Functional Allocation250

A.Linear and Nonlinear Activity Alloca-tion250

B.Similarities, Differences, Variations,and Choosing between Geographical and Activity Allocation251

Ⅵ.Miscellaneous Variations on the Basic Model254

A.Dealing with Inequality Constraints254

B.Dealing Differently with Crimes, Peo-ple, or Other Entities in Different Places256

Ⅶ.Some Conclusions258

Appendix 4A.Glossary of Terms271

Appendix 4B.Basic Formulas Used273

Part Ⅲ Problems that Can Be Viewed as Optimum-Mix or Optimum-Level Problems275

Chapter 5 A Linear-Programming Approach to Problems of Conflicting Legal Values, Like Free Press ver-sus Fair Trial281

Ⅰ.The Problem and the Data281

Ⅱ.Scoring the Cities and Respondents282

A.On the Occurrence of Free Press and Fair Trial282

B.On Satisfaction with Free Press and Fair Trial285

Ⅲ.The Problem Graphed286

A.The Axes and the Consumption-Pos-sibility Line286

B.The Legal Constraints288

Ⅳ.Some Solutions to the Problem289

A.For All Responding Groups Com-bined289

B.For Each Group Separately291

Ⅴ.Some Alternative or Supplementary Per-spectives on the Problem293

A.Emphasizing Optimum Level rather than Optimum Mix293

B.A Nonlinear, Diminishing-Returns Perspective297

C.Finding an Optimum Mix among Ap-proaches to Reducing Prejudicial Crime Reporting298

Ⅵ.Some Conclusions299

Appendix 5A.Glossary of Terms309

Appendix 5B.Basic Formulas Used311

Appendix 5C.Deriving a Multivariate Regres-sion Equation Where X1 + X2 = 1.0313

Index of Names317

Index of Subjects321

About the Authors329