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Fairness in Criminal Justice Risk Assessments: The State of the Art

Richard A. Berk, Hoda Heidari, Shahin Jabbari, Michael Kearns, Aaron Roth

arXiv:1703.09207v2stat.ML

TL;DR

Criminal justice risk-assessment fairness debates lack conceptual precision, especially when different fairness claims conflict. The paper integrates criminology, computer science, and statistics, using an arraignment-data illustration to examine fairness and accuracy. It concludes that multiple fairness criteria and accuracy cannot generally be maximized or satisfied simultaneously, making tradeoffs unavoidable.

  • Problem

    Fairness discussions in criminal justice risk assessments lack conceptual precision about competing fairness claims and their relationship to accuracy.

  • Method

    The paper integrates criminology, computer science, and statistics to examine fairness and accuracy and illustrates the analysis with arraignment data.

  • Results

    The paper identifies at least six kinds of fairness, some incompatible with one another and with accuracy, with differing base rates complicating comparisons across protected groups.

  • Takeaways & Limitations

    Fairness corrections require stakeholders to weigh competing values and legal considerations rather than relying on categorical endorsements or condemnations of risk assessments.

  • Takeaways & Limitations

    The paper reports no definitive technical or policy responses to fairness corrections and cautions against rushing stylized early results into policy.

Abstract

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Objectives: Discussions of fairness in criminal justice risk assessments typically lack conceptual precision. Rhetoric too often substitutes for careful analysis. In this paper, we seek to clarify the tradeoffs between different kinds of fairness and between fairness and accuracy. Methods: We draw on the existing literatures in criminology, computer science and statistics to provide an integrated examination of fairness and accuracy in criminal justice risk assessments. We also provide an empirical illustration using data from arraignments. Results: We show that there are at least six kinds of fairness, some of which are incompatible with one another and with accuracy. Conclusions: Except in trivial cases, it is impossible to maximize accuracy and fairness at the same time, and impossible simultaneously to satisfy all kinds of fairness. In practice, a major complication is different base rates across different legally protected groups. There is a need to consider challenging tradeoffs.

1 Introduction

Criminal justice risk assessments face unresolved fairness concerns because legitimate predictors can encode earlier unjust treatment. The paper therefore clarifies competing fairness concepts and their tradeoffs with accuracy.

  • 1 Introduction: Associations between protected-group indicators and legitimate predictors can encode unfairness even when race and gender are excluded.Prior criminal records may carry forward earlier unjust treatment by criminal justice actors and others.
  • 1 Introduction: Fairness concerns are difficult to reconcile without conceptual precision, allowing debates to become rhetorical rather than analytical.The authors link conceptual ambiguity to difficulty developing appropriate remedies and changing minds.
  • 1 Introduction: Accuracy is defined by out-of-sample prediction error, whereas fairness has multiple meanings that can conflict with one another and with accuracy.The paper emphasizes that accuracy is formally specified but fairness is not singular.
  • 1 Introduction: The paper examines formal fairness definitions, incompatibilities among them, effects on accuracy, and proposed algorithmic remedies.Its perspective draws primarily on statistics and computer science, which supply modern risk-assessment tools.
  • 1 Introduction: The paper does not translate formal fairness definitions into philosophical or jurisprudential notions because that multidisciplinary conversation is only beginning.Its overall conclusion is that tradeoffs between fairness concepts and accuracy are unavoidable.

2 Confusion Tables, Accuracy, and Fairness

The paper uses 2×2 confusion tables to distinguish several accuracy and fairness measures. Changing protected-group base rates can alter prediction errors, predicted distributions, and cost ratios even when within-group classification rates remain unchanged.

  • Confusion tables: A confusion table cross-tabulates actual binary outcomes against predicted outcomes, with failures treated as positive outcomes and successes as negative outcomes.The table’s margins and cells provide the basis for the paper’s accuracy and fairness calculations.
  • Accuracy measures: The framework distinguishes base rate, prediction distribution, overall procedure error, conditional procedure error, conditional use error, and cost ratio.These measures respectively describe outcome prevalence, predicted classes, total misclassification, errors conditional on actual outcomes, errors conditional on predictions, and the relative frequency of false negatives versus false positives.
  • Illustrative comparisons: A baseline example has false negative and false positive rates of .40, allowing the algorithm to identify known outcomes correctly 60% of the time with a 1 to 1 cost ratio.These quantities describe performance within the example table.
  • Illustrative comparisons: When the men’s success base rate changes from .50 to .33, false negative and false positive rates remain .40, but cross-group prediction errors and predicted distributions differ.The example changes only the top row of cell counts, leaving the bottom row unchanged.
  • Illustrative comparisons: Changing the base rate alone can create apparent unfairness and accuracy concerns, including unequal prediction errors, distribution mismatch, and different cost ratios.The paper emphasizes that these differences arise even when false negative and false positive rates within the tables are unaffected.
  • Illustrative comparisons: Equalizing one measure can worsen another: a revised table gives men a .40 success prediction error but a .20 false negative rate versus women’s .40.The example illustrates that correcting one disparity can produce better performance for one group on another measure.

3 The Statistical Framework

The statistical framework treats observed cases as realizations from a joint distribution and distinguishes population quantities from fitted estimates. This framework supports inference beyond the analyzed data but requires assumptions about how the data were generated.

  • Inference: Inference beyond the observed data requires a rationale for the data-generating process, a specified population, and an estimation target.The paper contrasts conventional population-parameter reasoning with broader joint-distribution formulations used in machine learning and related fields.
  • Population framework: The framework introduces a joint probability distribution P(Y, L, S) to represent a population of possible observations and their predictors and outcomes.This formulation is used to define the target population and support inference beyond the data on hand.
  • Population framework: A true response surface f(L, S) links predictors to the conditional expectation E(Y |L, S), while observed data are treated as IID realizations from the joint distribution.For categorical outcomes, the conditional expectation is a conditional probability.
  • Estimation: A fitting procedure h(L, S) is applied to data containing Y, producing fitted values that estimate the response surface through structures such as regression or gradient boosting.The paper distinguishes the fitting procedure, its optimization, and the resulting fitted values.
  • Estimation: The fitted function will generally be biased because legitimate predictors may be unavailable or measured with error, and the chosen functional form may be incorrect.The paper also notes that algorithmic procedures rarely provide asymptotically unbiased estimates for technical reasons.
  • Inference: Conventional statistical tests and confidence intervals can be invalidated by the estimation procedures, although reformulated inference with resampling can provide alternatives.The paper presents this as a technical limitation requiring later treatment.

4 Defining Fairness

The paper defines fairness through multiple comparisons of accuracy, prediction distributions, conditional errors, and error-cost ratios across protected groups. These criteria differ in technical meaning and cannot generally all be satisfied together.

  • Interpretive scope: The definitions share a concern with protected-group treatment but differ in substantive and technical details, and algorithmic information must be distinguished from decisions made using it.The paper focuses on algorithms rather than the separate question of how they affect decisions.
  • Fairness definitions: Overall accuracy equality compares total procedure accuracy across protected groups, while statistical parity compares their marginal distributions of predicted classes.Overall accuracy equality may require cost weighting when true positives and true negatives have different desirability.
  • Fairness definitions: Conditional procedure accuracy equality compares errors conditional on actual outcomes, whereas conditional use accuracy equality compares errors conditional on predicted outcomes.The former corresponds to equal false negative and false positive rates across groups; the latter concerns the accuracy of predicted outcomes.
  • Fairness definitions: Treatment equality requires the false-negative-to-false-positive ratio to be the same across protected groups, and these ratios can also serve as policy levers for other fairness goals.Different ratios may mean that the algorithm treats groups differently when correcting another disparity.
  • Fairness definitions: The paper distinguishes at least six fairness concepts, including overall accuracy equality, statistical parity, conditional procedure accuracy equality, conditional use accuracy equality, treatment equality, and total fairness.Total fairness requires satisfying the first five criteria simultaneously.
  • Limits of fairness criteria: Total fairness cannot be achieved in practice, and some additional fairness definitions cannot currently be operationalized usefully.The paper also notes that extending the definitions to more than two outcome categories requires additional statistical summaries.

5 Estimation Accuracy

The paper distinguishes estimating the true response surface from estimating an acknowledged approximation, with different implications for bias and asymptotic accuracy. Out-of-sample evaluation is needed to assess prediction accuracy, while finite-sample and procedural issues remain important.

  • Estimation targets: Larger samples reduce random estimation error, but estimates of the true response surface can still combine bias and variance.The gap between estimates and truth is not a conventional confidence interval because the truth is unknown.
  • Estimation targets: An acknowledged approximation to the population response surface can be estimated asymptotically without bias, with less random error as sample size increases.The same asymptotic logic applies to probabilities computed from the outcome-by-prediction cross-tabulation.
  • Accuracy assessment: Out-of-sample performance, such as generalization error or expected prediction error, is used to address estimation accuracy and avoid in-sample overfitting.Test data or methods that approximate test data are required for credible accuracy assessment.
  • Summary: The fitting procedure approximates the true response surface, so cross-tabulation probabilities inherit the strengths and weaknesses of the selected estimation target.Targeting the true surface retains bias, whereas targeting an acknowledged approximation permits asymptotically unbiased estimation.
  • Practical complications: Algorithm tuning, test-data availability, and disciplinary differences in estimation targets complicate practical accuracy assessment.These technical details are identified as beyond the paper’s scope.

6 Tradeoffs

Fairness criteria share the same confusion-table quantities, so they can conflict with one another and with accuracy. Different base rates and the absence of separation create the central impossibility and policy tradeoffs.

  • 6 Tradeoffs: Excluding a predictor associated non-redundantly with outcomes reduces accuracy and increases both false negatives and false positives.In parole decisions, this can mean more unnecessary detention and more inappropriate release.
  • 6 Tradeoffs: Different fairness criteria are related because they use shared confusion-table cell counts, creating tradeoffs among the criteria.The paper introduces these criteria through probability definitions that are equivalent to proportion-based formulations.
  • Fairness concepts: Calibration within groups requires predicted outcome proportions to match actual outcome proportions at each score value or among proximate scores.Unequal calibration can make decision-makers take one group’s predictions less seriously.
  • Fairness concepts: Base rates are the population probabilities of outcome classes, while separation means predictors permit perfectly accurate classification.These concepts determine when multiple fairness conditions can coexist.
  • 6.1 Some Proven “Impossibility Theorems”: When base rates differ and separation is absent, conditional use accuracy equality cannot coexist with equal false-positive and false-negative rates.Equal base rates or separation is required to achieve both conditions simultaneously.
  • Policy implications: With differing base rates and no separation, achieving conditional use accuracy equality requires accepting different false-positive and false-negative rates across groups.Conversely, equal error rates rule out conditional use accuracy equality, forcing stakeholders to choose between priorities.
  • 6.1.3 Perfect Separation: Perfect separation permits zero false-positive and false-negative rates alongside both conditional procedure and conditional use accuracy equality.The paper characterizes this as an ideal but fanciful setting.
  • 6.1.4 Closer To Real Life: In realistic settings, separation is virtually absent, although some fairness criteria can sometimes be achieved when base rates are cooperative.Equal base rates can support several fairness conditions, but such cases are rare in criminal justice applications.

7 Potential Solutions

The paper surveys preprocessing, in-processing, and post-processing strategies for addressing different forms of unfairness, while emphasizing that these remedies create technical and policy tradeoffs. No approach simultaneously resolves fairness concerns without potential costs to accuracy or other fairness criteria.

  • Potential Solutions: Three broad strategies address bias: preprocessing changes data before fitting, in-processing modifies classification or fitting, and post-processing adjusts predictions afterward.These strategies can also be combined when both fairness and accuracy are considered.
  • Pre-Processing: Preprocessing can remove associations between predictors and protected classes, but residualizing predictors may miss nonlinear or interaction effects unless they are explicitly modeled.Unanticipated higher-order interactions make this approach challenging when predictors and protected-class indicators interact.
  • Pre-Processing: Rebalancing base rates through group weights or relabeled outcomes may reduce disparities, but can lower accuracy and exchange one form of unfairness for another.The paper calls for numerically specifying the accuracy loss and disparity reduction before making such a choice.
  • Pre-Processing: A joint-distribution transformation can reduce dependence on protected-class membership while limiting distortion, but its mapping to fairness criteria and its accuracy cost remain unclear.The procedure aims to preserve the original predictor distribution and avoid substantially changing individual cases.
  • In-Processing: In-processing methods can impose explicit fairness tradeoffs or add fairness penalties, but may produce unequal error rates, nonconvex optimization, or other unintended unfairness.Penalty-based fitting can yield local solutions, while explicit tradeoffs may put a thumb on the scale between false positives and false negatives.
  • Post-Processing: Post-processing can enforce equalized odds by randomly reassignment of predicted labels, but accuracy and conditional-use accuracy decline as reassignment increases, especially with disparate base rates.The resulting performance may approach that of the worst-performing protected group, leaving everyone equally worse off.
  • Making Fairness Operational: Fairness corrections require choosing an equality benchmark, and that choice reflects policy preferences about the costs and benefits of criminal-justice outcomes.The paper concludes that technical corrections are agnostic about the target outcome unless a policy preference is built into the algorithm.
  • Future Work: Current remedies lack definitive technical or policy answers, so proposed improvements should be characterized accurately and evaluated against current practice.The authors caution against rushing stylized early results into policy while recognizing that small improvements may still matter.

8 A Brief Empirical Example of Fairness Tradeoffs With In-Processing

The empirical illustration uses arraignment data and separate random-forest models for Black and White individuals to examine fairness tradeoffs. Although conditional-use accuracy equality was closely approximated, the example produced sharply different error rates and competing fairness outcomes.

  • Empirical Example: The arraignment example forecasts whether a person will be arrested for a violent crime within 21 months, informing release or detention decisions.The illustration treats a predicted violent crime as likely leading to detention, while a predicted non-arrest may support release.
  • In-Processing: Random forests were applied separately to Black and White individuals, with the Black model tuned to match Whites' conditional-use accuracy.Stratified sampling by outcome classes was used while growing each tree.
  • In-Processing: Conditional-use accuracy equality was closely approximated without using race or residence zip code as predictors.Useful predictors included age, prior record, gender, arrest timing, and age at first adult charge.
  • Empirical Results: The illustration reports different base rates for Black and White offenders, with success rates of .89 and .94, respectively.The White re-arrest rate is .06, while Black offenders are more likely to be arrested for a violent crime after release.
  • Empirical Results: Despite conditional-use accuracy equality, false-negative and false-positive rates vary dramatically by race, producing competing claims of racial injustice.White violent offenders are more often misclassified as nonviolent, while nonviolent Black offenders are more often misclassified as violent.
  • Empirical Results: For Black offenders, the false-positive-to-false-negative ratio exceeds 4.2, whereas for White offenders the false-negative-to-false-positive ratio exceeds 3.1.These ratios indicate different error tradeoffs across the two groups, with the algorithm especially avoiding false negatives for Blacks.
  • Conclusion: The example shows that different fairness criteria can be incompatible, so selecting among their tradeoffs is ultimately a political decision.The authors report no technical solution without some price being paid.

9 Conclusions

Criminal justice risk-assessment fairness presents mathematically formal tradeoffs, especially when protected groups have different base rates. The authors recommend explicit, stakeholder-determined compromises and modest near-term improvements rather than categorical judgments.

  • Risk-assessment fairness problems are subtle, and tradeoffs between fairness and accuracy are mathematically unavoidable except in stylized examples.These tradeoffs have formal proofs, while practical complications can be greater.
  • Different base rates across protected groups can cascade through fairness assessments and create difficult tradeoffs.The paper identifies this as a particularly challenging practical problem.
  • Advanced statistical procedures can improve transparency, accuracy, and fairness, but categorical endorsements or condemnations are unhelpful.The paper presents these procedures as part of a long-term development of criminal justice risk assessments.
  • Fairness and other tradeoffs should be represented explicitly as adjustable tuning parameters, although substantial technical and conceptual challenges remain.The authors note that progress is underway on both technical implementation and the development of fairness measures.
  • Stakeholders must determine acceptable tradeoffs because these choices concern values, law, and political process rather than science alone.The paper frames questions about exchanging accuracy improvements for changes in error rates as stakeholder decisions.
  • Because solutions will not come quickly, modest improvements in accuracy, transparency, and fairness should be considered against current practice.Current practice is identified as the operational benchmark.
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