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arxiv: 2606.02198 · v1 · pith:H64JRQBNnew · submitted 2026-06-01 · 💻 cs.LG · cs.CY

Model Multiplicity and Predictive Arbitrariness in Recidivism Risk Assessment

Ashwin Singh , Carlos Castillo This is my paper

Pith reviewed 2026-06-28 15:41 UTC · model grok-4.3

classification 💻 cs.LG cs.CY
keywords recidivism risk assessmentpredictive multiplicitymodel arbitrarinessinterpretable modelserror rate disparitiesmachine learningdecision support system
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The pith

Multiple accurate recidivism models agree on predictions far more than worst-case theory requires.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines whether multiple machine learning models for recidivism risk, each with similar accuracy, produce conflicting predictions for the same person and create arbitrary decisions. By encoding legal rules into labels for thousands of inmate releases, the authors build a dataset and train interpretable models that raise accuracy, shrink group error disparities, and make risk scores fall with rehabilitation. They first derive a tight lower bound on the average predictive agreement any finite collection of models must achieve, then measure how much real models with different coefficients actually disagree. Experiments show that agreement stays substantially above the theoretical floor, so multiplicity remains limited, and a rule that gives each inmate the lowest risk score from the set cuts arbitrariness without harming performance.

Core claim

The authors establish that in recidivism risk assessment the existence of many similarly accurate models with comparable error-rate disparities does not necessarily produce severe predictive multiplicity. A derived tight lower bound on expected predictive agreement is not realized in practice; empirical models exhibit substantially higher agreement than the bound guarantees. Assigning each inmate the lowest risk score among the models resolves predictive arbitrariness while preserving the models' performance and fairness properties.

What carries the argument

The tight lower bound on expected predictive agreement of any finite set of models over a dataset, together with the min-risk assignment policy that selects the lowest predicted risk for each individual.

Load-bearing premise

The algorithmically generated post-release labels accurately match the true recidivist or non-recidivist outcomes that would be observed in practice.

What would settle it

Collecting fresh post-release recidivism records for a new cohort and finding that the models disagree on those real labels at rates close to the theoretical lower bound would falsify the empirical claim of substantially higher agreement.

Figures

Figures reproduced from arXiv: 2606.02198 by Ashwin Singh, Carlos Castillo.

Figure 2
Figure 2. Figure 2: Empirical CDF of Self-Consistency on the test set [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Observed versus worst-case expected self [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Expected self-consistency as a function of average [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Variance in feature coefficients across the model pool for [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: A lowest-risk policy over the aggregated model pool P achieves higher balanced accuracy than the best FairSLIM solution (lowest ∆EO) on the test set, while demonstrating comparable error-rate parity (∆EO) for ϵ ≤ .03. predictive multiplicity. In actuarial risk assessment, the scoring rule underlying a model is typically not visible to incarcerated individuals, or the prison staff responsible for evaluating… view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of policies for resolving predictive multiplicity over the aggregated model pool [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Convergence behavior of SLIM. Although the solver does not converge within the allotted time, the majority of improvement in the objective occurs within the first 30 minutes, with only marginal gains thereafter. E Bound for Expected Self-Consistency In this section, we restate our bound on expected self￾consistency given in the paper, followed by its proof. For notational convenience, we encode predictions… view at source ↗
Figure 9
Figure 9. Figure 9: Convergence behavior of FairSLIM across different Rashomon tolerances [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Expected self-consistency of the model pool returned by [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Expected self-consistency of the model pool returned by [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Expected self-consistency of the model pool returned by [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
read the original abstract

Prediction tasks over individual futures, which are inherently noisy, often admit multiple similarly accurate models. When these models produce different predictions for the same individual, they raise concerns of arbitrariness in decision-making. How severe can this arbitrariness be, in theory and in practice? How can it be resolved to support high-stakes risk assessment? We address these questions through a study of a machine learning-based decision support system for recidivism risk assessment that has been in use for over 15 years. By translating complex legal rules into an algorithm for labeling post release outcomes (recidivist or non-recidivist), we first construct a dataset of thousands of inmate releases. Using this dataset, we learn interpretable models that improve predictive performance, reduce error-rate disparities between groups, and ensure that rehabilitative progress lowers risk scores. Next, we study predictive multiplicity, by first deriving a tight lower bound on the expected predictive agreement of any finite set of models over a dataset, and then by evaluating the extent to which structural diversity (e.g., different model coefficients) within this set translates to predictive multiplicity (i.e., different predictions for the same individual). Our experiments indicate that the existence of many similarly accurate models with comparable error-rate disparities does not necessarily translate into severe predictive multiplicity. Empirically, similarly performant models can exhibit substantially higher predictive agreement than worst-case theoretical guarantees suggest. We find that a simple policy that assigns each inmate the lowest risk among these models is effective for addressing predictive arbitrariness.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper constructs a recidivism dataset by translating legal rules into an algorithmic procedure for labeling post-release outcomes as recidivist or non-recidivist. It trains interpretable models that improve predictive performance, reduce error-rate disparities, and incorporate rehabilitative progress. It derives a tight lower bound on expected predictive agreement for any finite set of models and evaluates structural diversity versus predictive multiplicity on the dataset, concluding that similarly accurate models exhibit substantially higher agreement than the worst-case bound and that a min-risk policy mitigates arbitrariness.

Significance. If the constructed labels are a faithful proxy for observed recidivism, the work supplies a parameter-free theoretical bound on agreement together with empirical evidence that multiplicity is milder than worst-case analysis predicts in this domain, plus a simple mitigation policy. This would strengthen the literature on model multiplicity for high-stakes risk assessment.

major comments (2)
  1. [Abstract, paragraph 2] Abstract, paragraph 2: all empirical claims (higher-than-bound agreement rates, effectiveness of the lowest-risk policy, error-rate disparity measurements) are computed exclusively on labels produced by an algorithmic translation of legal rules. No comparison to actual observed post-release recidivism events, no sensitivity analysis to labeling-rule perturbations, and no external validation are described; this is load-bearing for the central empirical conclusion that real models exceed the theoretical guarantee.
  2. [Lower-bound derivation (referenced in abstract)] The derivation of the tight lower bound on expected predictive agreement is presented as independent of the data-generating process, yet the subsequent claim that observed models exceed this bound is evaluated only on the same constructed distribution. Without an explicit statement of the assumptions under which the bound remains tight when the label distribution is itself algorithmically defined, the reported gap between theory and experiment cannot be interpreted as evidence about real recidivism.
minor comments (1)
  1. [Abstract] Abstract provides no equations for the lower bound, no dataset size or class-balance statistics, and no error bars or confidence intervals on the reported agreement rates or policy performance.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments on the manuscript. Below we respond point-by-point to the two major comments, clarifying the scope of our empirical claims on the rule-constructed dataset and proposing targeted revisions to the abstract, theoretical section, and discussion to address concerns about interpretation and assumptions.

read point-by-point responses

  1. Referee: [Abstract, paragraph 2] Abstract, paragraph 2: all empirical claims (higher-than-bound agreement rates, effectiveness of the lowest-risk policy, error-rate disparity measurements) are computed exclusively on labels produced by an algorithmic translation of legal rules. No comparison to actual observed post-release recidivism events, no sensitivity analysis to labeling-rule perturbations, and no external validation are described; this is load-bearing for the central empirical conclusion that real models exceed the theoretical guarantee.

    Authors: We agree that all reported empirical results, including agreement rates, the min-risk policy, and disparity measurements, rely exclusively on the dataset whose labels were produced by algorithmic translation of legal rules. The manuscript does not include comparisons to observed post-release events, sensitivity analyses, or external validation. We will revise the abstract, introduction, and conclusion to explicitly state that the empirical findings apply to this constructed proxy and do not claim correspondence to real observed recidivism without additional validation. This is a partial revision that tempers the interpretation while preserving the paper's focus on multiplicity within the studied setting. revision: partial

  2. Referee: [Lower-bound derivation (referenced in abstract)] The derivation of the tight lower bound on expected predictive agreement is presented as independent of the data-generating process, yet the subsequent claim that observed models exceed this bound is evaluated only on the same constructed distribution. Without an explicit statement of the assumptions under which the bound remains tight when the label distribution is itself algorithmically defined, the reported gap between theory and experiment cannot be interpreted as evidence about real recidivism.

    Authors: The lower bound is a purely mathematical result on the minimum expected agreement for any finite collection of models given their accuracies; it holds for arbitrary label distributions and makes no reference to how labels are generated. We will insert an explicit clarifying statement in the theoretical section noting that the bound's tightness is with respect to worst-case model sets and is independent of the label-generation mechanism. We will also revise the abstract and discussion to limit claims about the observed gap to the constructed distribution, removing any implication that the gap constitutes evidence about real recidivism beyond the proxy. This revision will be made. revision: yes

Circularity Check

0 steps flagged

No circularity: theoretical bound derived independently; empirical evaluation uses externally constructed labels

full rationale

The paper first derives a lower bound on expected predictive agreement as a general theoretical result applying to any finite set of models, then separately constructs a dataset via algorithmic translation of legal rules (independent of model training) and evaluates agreement on models fit to that dataset. No quoted step reduces a claimed prediction or first-principles result to a fitted parameter, self-citation chain, or definitional renaming; the bound is presented as worst-case and the empirical excess over the bound is measured on proxy labels whose construction does not embed the multiplicity statistics.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Because only the abstract is available, the ledger is necessarily incomplete; the central claims rest on the validity of the legal-rule-to-label translation and on the assumption that the learned models belong to a class for which the agreement bound applies.

axioms (1)
  • domain assumption The algorithm that translates complex legal rules into recidivist/non-recidivist labels produces ground-truth outcomes that match what would be observed in practice.
    Invoked when the authors state they construct a dataset of thousands of inmate releases (abstract, paragraph 2).

pith-pipeline@v0.9.1-grok · 5801 in / 1434 out tokens · 20554 ms · 2026-06-28T15:41:24.675754+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

44 extracted references · 18 canonical work pages

  1. [1]

    Statistical Modeling: The Two Cultures , urldate =

    Leo Breiman , journal =. Statistical Modeling: The Two Cultures , urldate =

  2. [2]

    Setting the

    Jackson, Eugenie and Mendoza, Christina , journal =. Setting the. 2020 , month =

    2020

  3. [3]

    2023 , month = jul, day =

    Hamilton, Melissa and Ugwudike, Pamela , title =. 2023 , month = jul, day =

    2023

  4. [4]

    Proceedings of the 38th International Conference on Machine Learning , pages =

    Characterizing Fairness Over the Set of Good Models Under Selective Labels , author =. Proceedings of the 38th International Conference on Machine Learning , pages =. 2021 , editor =

    2021

  5. [5]

    Proceedings of the 41st International Conference on Machine Learning , pages =

    Position: Amazing Things Come From Having Many Good Models , author =. Proceedings of the 41st International Conference on Machine Learning , pages =. 2024 , editor =

    2024

  6. [6]

    Journal of Machine Learning Research , year =

    Aaron Fisher and Cynthia Rudin and Francesca Dominici , title =. Journal of Machine Learning Research , year =

  7. [7]

    doi: 10.1145/3531146.3533143

    Black, Emily and Raghavan, Manish and Barocas, Solon , title =. Proceedings of the 2022 ACM Conference on Fairness, Accountability, and Transparency , pages =. 2022 , isbn =. doi:10.1145/3531146.3533149 , abstract =

    work page doi:10.1145/3531146.3533149 2022

  8. [8]

    and Kim, Yea-Seul and D'Antoni, Loris and Albarghouthi, Aws , title =

    Meyer, Anna P. and Kim, Yea-Seul and D'Antoni, Loris and Albarghouthi, Aws , title =. Proceedings of the 2025 CHI Conference on Human Factors in Computing Systems , articleno =. 2025 , isbn =. doi:10.1145/3706598.3713524 , abstract =

    work page doi:10.1145/3706598.3713524 2025

  9. [9]

    Proceedings of the AAAI/ACM Conference on AI, Ethics, and Society , author=

    Systemizing Multiplicity: The Curious Case of Arbitrariness in Machine Learning , volume=. Proceedings of the AAAI/ACM Conference on AI, Ethics, and Society , author=. 2025 , month=. doi:10.1609/aies.v8i2.36609 , number=

    work page doi:10.1609/aies.v8i2.36609 2025

  10. [10]

    Proceedings of the AAAI/ACM Conference on AI, Ethics, and Society , author=

    Fairness and Sparsity Within Rashomon Sets: Enumeration-Free Exploration and Characterization , volume=. Proceedings of the AAAI/ACM Conference on AI, Ethics, and Society , author=. 2025 , month=. doi:10.1609/aies.v8i2.36653 , number=

    work page doi:10.1609/aies.v8i2.36653 2025

  11. [11]

    The RisCanvi , booktitle =

    Andrés-Pueyo, Antonio and Arbach-Lucioni, Karin and Redondo, Santiago , publisher =. The RisCanvi , booktitle =. doi:https://doi.org/10.1002/9781119184256.ch13 , url =. https://onlinelibrary.wiley.com/doi/pdf/10.1002/9781119184256.ch13 , year =

    work page doi:10.1002/9781119184256.ch13

  12. [12]

    Fairness through awareness

    Dwork, Cynthia and Hardt, Moritz and Pitassi, Toniann and Reingold, Omer and Zemel, Richard , title =. Proceedings of the 3rd Innovations in Theoretical Computer Science Conference , pages =. 2012 , isbn =. doi:10.1145/2090236.2090255 , abstract =

    work page doi:10.1145/2090236.2090255 2012

  13. [13]

    Equality of Opportunity in Supervised Learning , url =

    Hardt, Moritz and Price, Eric and Srebro, Nati , booktitle =. Equality of Opportunity in Supervised Learning , url =

  14. [14]

    Fairness and Machine Learning: Limitations and Opportunities , author =

  15. [15]

    Advances in neural information processing systems , volume=

    Exploring and interacting with the set of good sparse generalized additive models , author=. Advances in neural information processing systems , volume=

  16. [16]

    and Ustun, Berk , year=

    Watson-Daniels, Jamelle and Parkes, David C. and Ustun, Berk , year=. Predictive Multiplicity in Probabilistic Classification , volume=. doi:10.1609/aaai.v37i9.26227 , booktitle=

    work page doi:10.1609/aaai.v37i9.26227

  17. [17]

    Proceedings of the 37th International Conference on Machine Learning , pages =

    Predictive Multiplicity in Classification , author =. Proceedings of the 37th International Conference on Machine Learning , pages =. 2020 , editor =

    2020

  18. [18]

    Proceedings of the 2024 ACM Conference on Fairness, Accountability, and Transparency , pages =

    Gillis, Talia B and Meursault, Vitaly and Ustun, Berk , title =. Proceedings of the 2024 ACM Conference on Fairness, Accountability, and Transparency , pages =. 2024 , isbn =. doi:10.1145/3630106.3658912 , abstract =

    work page doi:10.1145/3630106.3658912 2024

  19. [19]

    , title =

    Dai, Gordon and Ravishankar, Pavan and Yuan, Rachel and Black, Emily and Neill, Daniel B. , title =. Proceedings of the 5th ACM Conference on Equity and Access in Algorithms, Mechanisms, and Optimization , pages =. 2025 , isbn =. doi:10.1145/3757887.3763011 , abstract =

    work page doi:10.1145/3757887.3763011 2025

  20. [20]

    Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency , pages =

    Black, Emily and Fredrikson, Matt , title =. Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency , pages =. 2021 , isbn =. doi:10.1145/3442188.3445894 , abstract =

    work page doi:10.1145/3442188.3445894 2021

  21. [21]

    Proceedings of the AAAI Conference on Artificial Intelligence , author=

    Arbitrariness and Social Prediction: The Confounding Role of Variance in Fair Classification , volume=. Proceedings of the AAAI Conference on Artificial Intelligence , author=. 2024 , month=. doi:10.1609/aaai.v38i20.30203 , abstractNote=

    work page doi:10.1609/aaai.v38i20.30203 2024

  22. [22]

    A Path to Simpler Models Starts With Noise , url =

    Semenova, Lesia and Chen, Harry and Parr, Ronald and Rudin, Cynthia , booktitle =. A Path to Simpler Models Starts With Noise , url =

  23. [23]

    Proceedings of the international AAAI conference on web and social media , volume=

    Big questions for social media big data: Representativeness, validity and other methodological pitfalls , author=. Proceedings of the international AAAI conference on web and social media , volume=

  24. [24]

    2016 , journal=

    Machine bias , author=. 2016 , journal=

    2016

  25. [25]

    Regulation (EU) 2024/1689 of the European Parliament and of the Council of 13 June 2024 laying down harmonised rules on artificial intelligence (Artificial Intelligence Act) , year =

    2024

  26. [26]

    2022 , address =

    Karimi-Haghighi, Marzieh , title =. 2022 , address =

    2022

  27. [27]

    Machine Learning , year =

    Ustun, Berk and Rudin, Cynthia , title =. Machine Learning , year =. doi:10.1007/s10994-015-5528-6 , url =

    work page doi:10.1007/s10994-015-5528-6

  28. [28]

    Harvard Data Science Review , volume=

    The age of secrecy and unfairness in recidivism prediction , author=. Harvard Data Science Review , volume=. 2020 , publisher=

    2020

  29. [29]

    arXiv preprint arXiv:2106.05498 , year=

    It's compaslicated: The messy relationship between rai datasets and algorithmic fairness benchmarks , author=. arXiv preprint arXiv:2106.05498 , year=

    arXiv

  30. [30]

    Georgetown Law Journal , year =

    Black, Emily and Koepke, John Logan and Kim, Pauline and Barocas, Solon and Hsu, Mingwei , title =. Georgetown Law Journal , year =. doi:10.2139/ssrn.4590481 , url =

    work page doi:10.2139/ssrn.4590481

  31. [31]

    Proceedings of the AAAI/ACM Conference on AI, Ethics, and Society , volume=

    Algorithmic fairness from the perspective of legal anti-discrimination principles , author=. Proceedings of the AAAI/ACM Conference on AI, Ethics, and Society , volume=

  32. [32]

    The Modern Law Review , volume =

    Adams-Prassl, Jeremias and Binns, Reuben and Kelly-Lyth, Aislinn , title =. The Modern Law Review , volume =. doi:https://doi.org/10.1111/1468-2230.12759 , url =. https://onlinelibrary.wiley.com/doi/pdf/10.1111/1468-2230.12759 , abstract =

    work page doi:10.1111/1468-2230.12759

  33. [33]

    Andrews, D. A. and Bonta, James and Hoge, R. D. , title =. Criminal Justice and Behavior , volume =. 1990 , doi =

    1990

  34. [34]

    Artificial Intelligence and Law , year =

    Portela, Manuel and Castillo, Carlos and Tolan, Song. Artificial Intelligence and Law , year =. doi:10.1007/s10506-024-09393-y , url =

    work page doi:10.1007/s10506-024-09393-y

  35. [35]

    Proceedings of the Conference on Fairness, Accountability, and Transparency , pages =

    Ustun, Berk and Spangher, Alexander and Liu, Yang , title =. Proceedings of the Conference on Fairness, Accountability, and Transparency , pages =. 2019 , isbn =. doi:10.1145/3287560.3287566 , abstract =

    work page doi:10.1145/3287560.3287566 2019

  36. [36]

    Proceedings of the 1st Conference on Fairness, Accountability and Transparency , pages =

    Interventions over Predictions: Reframing the Ethical Debate for Actuarial Risk Assessment , author =. Proceedings of the 1st Conference on Fairness, Accountability and Transparency , pages =. 2018 , editor =

    2018

  37. [37]

    2017 , month = jun, day =

    Wexler, Rebecca , title =. 2017 , month = jun, day =

    2017

  38. [38]

    2024 , publisher=

    Algorithmic institutionalism: the changing rules of social and political life , author=. 2024 , publisher=

    2024

  39. [39]

    Criminal Justice and Behavior , volume =

    Zachary Hamilton and Alex Kigerl and Michael Campagna and Robert Barnoski and Stephen Lee and Jacqueline van Wormer and Lauren Block , title =. Criminal Justice and Behavior , volume =. 2016 , doi =

    2016

  40. [40]

    Hoffman , abstract =

    Peter B. Hoffman , abstract =. Twenty years of operational use of a risk prediction instrument: The United States parole commission's salient factor score , journal =. 1994 , issn =. doi:https://doi.org/10.1016/0047-2352(94)90090-6 , url =

    work page doi:10.1016/0047-2352(94)90090-6 1994

  41. [41]

    The age and crime relationship: Social variation, social explanations

    Ulmer, \ Jeffery T.\ and Darrell Steffensmeier. The age and crime relationship: Social variation, social explanations. The Nurture Versus Biosocial Debate in Criminology. 2014. doi:10.4135/9781483349114.n23

    work page doi:10.4135/9781483349114.n23 2014

  42. [42]

    CatBoost: unbiased boosting with categorical features , url =

    Prokhorenkova, Liudmila and Gusev, Gleb and Vorobev, Aleksandr and Dorogush, Anna Veronika and Gulin, Andrey , booktitle =. CatBoost: unbiased boosting with categorical features , url =

  43. [43]

    2024 , month = jan, url =

    2024

  44. [44]

    2026 , month = mar, day =

    Jimenez Arandia, Pablo , title =. 2026 , month = mar, day =

    2026