🤖 machine learning

Model Multiplicity and Predictive Arbitrariness in Recidivism Risk Assessment

This paper investigates predictive arbitrariness in recidivism risk assessment by demonstrating that, despite the existence of multiple similarly accurate models, their predictions often exhibit substantial agreement in practice, and proposes a policy of assigning the lowest risk score among these models as an effective solution to mitigate decision-making inconsistencies.

Original authors: Ashwin Singh, Carlos Castillo

Published 2026-06-02

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CC BY 4.0

Original authors: Ashwin Singh, Carlos Castillo

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are a judge trying to decide if a prisoner should be released early. You have a computer program that gives the prisoner a "risk score" to predict if they will commit another crime. This is the real-world situation the paper tackles, specifically looking at a system used in Catalonia, Spain, called RisCanvi.

Here is the story of the paper, broken down into simple concepts and analogies.

1. The Problem: The "Rashomon" Effect

In the movie Rashomon, four different witnesses tell four completely different stories about the same crime, yet all stories seem plausible.

The authors found that machine learning models suffer from the same problem. When trying to predict if a prisoner will re-offend, there isn't just one "correct" math formula. There are many different formulas that are all equally good at predicting the past.

The Issue: If you have two equally smart formulas, but they give different answers for the same person (one says "Low Risk," the other says "High Risk"), the decision becomes arbitrary. It feels like rolling a dice to decide someone's future. This is called Predictive Multiplicity.

2. The Fix: Cleaning the Data First

Before building better formulas, the authors realized the "textbook" the computer was studying was messy.

The Old Way: The current system (RisCanvi) was trained on data that was often outdated or labeled incorrectly because it was hard to track if someone actually committed a new crime after release (due to legal delays). It was like trying to learn to drive using a map from 1990.
The New Way: The authors worked with legal experts to write a computer program that strictly followed the complex legal rules to label the data correctly. They created a massive, clean dataset of 17,500 prisoners. This is like giving the computer a brand-new, high-definition GPS map.

3. Building Better Models: The "Fair Scorecard"

Using this clean data, the authors built new models. They didn't just want them to be accurate; they wanted them to be fair and logical.

Logic: They made sure the model followed common sense: if a prisoner gets a degree or learns a trade (rehabilitation), their risk score must go down. If they have bad habits, it goes up.
Fairness: They ensured the model didn't unfairly punish specific groups (like foreigners vs. locals) more than others.

4. The Big Discovery: "Many Paths, Same Destination"

This is the most surprising part of the paper. The authors gathered a huge group of these "equally smart, fair" models (a "Rashomon Set") and asked: Do they all disagree with each other?

The Answer: No.

The Analogy: Imagine a group of 100 expert navigators trying to guide a ship through a foggy sea. You might expect them to all point in different directions. Instead, the authors found that 91% of the time, all 100 navigators agreed on the exact same direction.
The Catch: They only disagreed on the few cases that were right on the edge of the "fog" (the decision boundary). For the vast majority of prisoners, the models were in total agreement.
The Lesson: Just because there are many different math formulas doesn't mean the predictions are chaotic. The "arbitrariness" is much smaller than theory suggests.

5. The Solution: The "Benefit of the Doubt" Rule

So, what do you do for the small group of prisoners where the models do disagree?
The authors propose a simple policy called the "Lowest-Risk Policy" (or Favor Rei, a legal principle meaning "favor the defendant").

How it works: If Model A says "High Risk" and Model B says "Low Risk," you simply pick the Low Risk score.
Why it works: It acts like a safety net. It ensures that if there is any doubt, the prisoner gets the benefit of the doubt.
The Result: This simple rule actually made the system more accurate and fairer than using a single complex model or averaging all the models together. It reduced the number of people wrongly labeled as high-risk without letting dangerous people slip through.

Summary

The paper argues that we don't need to fear having many different AI models for predicting crime.

Clean your data first (stop using messy, old maps).
Build models that are fair and logical.
Realize that even with many different models, they usually agree on the answer.
When they disagree, use a simple rule: Pick the safest, lowest-risk option.

This approach turns a confusing mess of "arbitrary" predictions into a reliable, fair, and logical tool for the justice system.

Technical Summary: Model Multiplicity and Predictive Arbitrariness in Recidivism Risk Assessment

Problem Statement

The paper addresses the challenge of predictive multiplicity (often referred to as the Rashomon Effect) in high-stakes criminal recidivism risk assessment. In noisy prediction tasks, multiple models with comparable accuracy often exist, yet they may produce divergent predictions for the same individual. This creates predictive arbitrariness, raising concerns about fairness and consistency in judicial decision-making.

Specifically, the authors investigate the RisCanvi system, a decision support tool used in Catalonia since 2009. The current system faces several critical issues:

Data Quality: Reliance on outdated training data and complex, error-prone manual labeling of recidivism (distinguishing between re-incarceration for new crimes vs. technical violations or pre-existing sentences).
Performance Disparities: The existing logistic regression model exhibits high false negative rates and significant error-rate disparities between demographic groups (e.g., nationals vs. foreigners).
Lack of Monotonicity: The current system does not guarantee that rehabilitative progress (dynamic features) leads to lower risk scores, a requirement for fair rehabilitation incentives.
Arbitrariness: Even if a "less discriminatory" model is found, the existence of a "Rashomon Set" (a set of models with similar performance) implies that different valid models could yield different risk scores for the same inmate, undermining the reliability of the assessment.

Methodology

1. Dataset Construction

The authors developed a rigorous labeling algorithm to construct a high-quality dataset of 17,542 inmate releases from Catalan prisons (2010–2019).

Labeling Process: They translated complex legal rules defining "penal recidivism" (sentencing to prison for a new crime) into an iterative algorithm. This algorithm was refined through collaboration with sentence enforcement experts until it matched human expert annotations.
Features: The dataset includes 43 features per release (20 static, e.g., age at onset; 23 dynamic, e.g., education level) from the inmate's final evaluation.
Split: A chronological train-test split was used (Train: 2010–2018; Test: 2019) to ensure temporal validity.

2. Optimization Framework (FairSLIM)

The authors propose a two-step Mixed-Integer Linear Programming (MILP) framework:

Step 1: SLIM with Monotonicity: They utilize the SLIM (Supersparse Linear Integer Model) formulation to learn a linear integer scoring system. Crucially, they enforce monotonicity constraints by restricting feature coefficients to non-negative integers. This ensures that adverse static features increase risk, while positive dynamic features (rehabilitative progress) decrease risk.
Step 2: Exploring the Rashomon Set: Building on the work of Langlade et al. (2025), they search the $\epsilon$ -Rashomon Set (models with empirical risk within $\epsilon$ $ϵ$ of the optimal) for Less Discriminatory Models (LDMs).
- They generalize the search for $m > 2$ demographic groups.
- They minimize the Equalized Odds violation ( $\Delta EO$ ), defined as the maximum pairwise disparity in False Positive Rates (FPR) and False Negative Rates (FNR) across groups.
- They optimize this by tracking min/max FPR/FNR across groups, reducing fairness constraints from $O(m^2)$ to $O(m)$ .

3. Analyzing Predictive Multiplicity

To quantify arbitrariness, the authors extend the concept of self-consistency (Cooper et al., 2024) to the Rashomon Set:

Definition: For a finite set of models $P$ , self-consistency $SCP(x)$ is the probability that two models drawn uniformly at random from $P$ agree on the prediction for instance $x$ .
Theoretical Bound: They derive a tight lower bound on expected self-consistency (Proposition 1) based on the average 0-1 loss of the model pool. This bound represents the worst-case scenario for agreement.
Policy Evaluation: They evaluate three policies to resolve multiplicity:
1. Ensembling: Averaging predictions.
2. Random Selection: Picking a random model for each instance.
3. Lowest-Risk Policy (LRP): Assigning the inmate the lowest risk score predicted by any model in the pool (aligning with the favor rei principle).

Key Results

1. Predictive Performance and Fairness

Superiority over Baselines: The proposed models (SLIM and FairSLIM) significantly outperform the operational RisCanvi model. While RisCanvi achieves high accuracy by predicting the majority class, it suffers from a high false negative rate (84.7%) and poor balanced accuracy (56.2%).
Interpretable Models: The new linear integer models achieve balanced accuracies of ~70–73% and reduce the false negative rate by over 65%.
Fairness: Searching for LDMs within 1% of the optimal risk ( $\epsilon \le 0.01$ ) reduces the maximum error-rate disparity ( $\Delta EO$ ) between subgroups to 5% on the test set. This performance is comparable to or better than a complex CatBoost baseline, while maintaining interpretability.

2. Predictive Multiplicity and Self-Consistency

High Agreement: Despite the existence of many structurally diverse models (with varying coefficients for static and dynamic features), the observed self-consistency is 91%. This is significantly higher than the theoretical worst-case lower bound (0.53).
Disagreement Location: Predictive disagreement is concentrated almost exclusively on instances near the decision boundary (low-margin instances). For high-margin instances, models agree perfectly.
Structural Diversity vs. Predictive Agreement: The study demonstrates that high structural diversity (different coefficients) does not necessarily translate to severe predictive multiplicity.

3. Efficacy of the Lowest-Risk Policy

The Lowest-Risk Policy (FairSLIM-LRP) assigns the lowest risk score among the pool of valid models to each inmate.
Performance: This policy achieves the highest balanced accuracy (71.2%) among all resolution mechanisms tested (including ensembling and random selection) while maintaining comparable error-rate parity.
Implication: By selecting the most favorable outcome among valid models, the system reduces arbitrariness without sacrificing predictive utility or fairness.

Significance and Claims

The paper claims several contributions to the field of algorithmic fairness and risk assessment:

Generalization of Fairness Constraints: It generalizes the search for less discriminatory models in the Rashomon Set to $m > 2$ subgroups with only $O(m)$ additional constraints, making it computationally feasible for complex demographic partitions.
Theoretical Bound on Arbitrariness: It provides a tight lower bound on expected self-consistency for any finite set of binary classifiers, offering a theoretical benchmark to compare against empirical agreement.
Real-World Case Study: It presents the first real-world study of predictive multiplicity in recidivism risk assessment, moving beyond theoretical simulations to a deployed system (RisCanvi).
Policy Recommendation: It proposes and validates a Lowest-Risk Policy as an effective mechanism to resolve predictive arbitrariness. This approach aligns with the legal principle of favor rei (in doubt, favor the defendant) and the anti-subordination principle, addressing systemic biases by actively choosing the least punitive valid prediction.
Data Quality Impact: The work highlights that automating the labeling of post-release outcomes using legal rules yields a dataset 17 times larger than the current training set, materially improving model performance and fairness.

The authors conclude that while model multiplicity is a theoretical concern, in practice, the resulting arbitrariness is often limited to a small fraction of cases near the decision boundary. Therefore, simple, principled policies like the Lowest-Risk Policy can effectively mitigate arbitrariness while preserving the benefits of exploring a diverse set of fair models.