# Reconciling Individual Probability Forecasts

arXiv: https://arxiv.org/abs/2209.01687 · HTML: https://mlsanity.com/paper/2209.01687/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 43 references that are in the map.
- First posted on arXiv 4 Sep 2022.

## Builds on (most cited first, 11 of 11)

- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [Predictive Multiplicity in Classification](https://mlsanity.com/paper/1909.06677/) (2019)
- [Algorithmic Stability for Adaptive Data Analysis](https://mlsanity.com/paper/1511.02513/) (2015)
- [Generalization in Adaptive Data Analysis and Holdout Reuse](https://mlsanity.com/paper/1506.02629/) (2015)
- [Outcome Indistinguishability](https://mlsanity.com/paper/2011.13426/) (2020)
- [Practical Adversarial Multivalid Conformal Prediction](https://mlsanity.com/paper/2206.01067/) (2022)
- [Moment Multicalibration for Uncertainty Estimation](https://mlsanity.com/paper/2008.08037/) (2020)
- [Online Multivalid Learning: Means, Moments, and Prediction Intervals](https://mlsanity.com/paper/2101.01739/) (2021)
- [A New Analysis of Differential Privacy's Generalization Guarantees](https://mlsanity.com/paper/1909.03577/) (2019)
- [An Algorithmic Framework for Bias Bounties](https://mlsanity.com/paper/2201.10408/) (2022)
- [Tracking and Improving Information in the Service of Fairness](https://mlsanity.com/paper/1904.09942/) (2019)

## Built on by (most cited first, 14 of 14)

- [Dropout-Based Rashomon Set Exploration for Efficient Predictive Multiplicity Estimation](https://mlsanity.com/paper/2402.00728/) (2024)
- [The Dataset Multiplicity Problem: How Unreliable Data Impacts Predictions](https://mlsanity.com/paper/2304.10655/) (2023)
- [Recourse under Model Multiplicity via Argumentative Ensembling (Technical Report)](https://mlsanity.com/paper/2312.15097/) (2023)
- [Multi-Target Multiplicity: Flexibility and Fairness in Target Specification under Resource Constraints](https://mlsanity.com/paper/2306.13738/) (2023)
- [Be Intentional About Fairness!: Fairness, Size, and Multiplicity in the Rashomon Set](https://mlsanity.com/paper/2501.15634/) (2025)
- [Networked Information Aggregation via Machine Learning](https://mlsanity.com/paper/2507.09683/) (2025)
- [Arbitrariness Lies Beyond the Fairness-Accuracy Frontier](https://mlsanity.com/paper/2306.09425/) (2023)
- [Reconciling Model Multiplicity for Downstream Decision Making](https://mlsanity.com/paper/2405.19667/) (2024)
- [The Costs of Pretending That There Are Data-Generating Probability Distributions in the Social World](https://mlsanity.com/paper/2407.17395/) (2024)
- [The Role of Hyperparameters in Predictive Multiplicity](https://mlsanity.com/paper/2503.13506/) (2025)
- [Does calibration mean what they say it means; or, the reference class problem rises again](https://mlsanity.com/paper/2412.16769/) (2024)
- [Argumentative Ensembling for Robust Recourse under Model Multiplicity](https://mlsanity.com/paper/2506.20260/) (2025)
- [Reconciling Predictive Multiplicity in Practice](https://mlsanity.com/paper/2501.16549/) (2025)
- [Trustworthy AI: Ensuring Reliability and Accountability from Models to Agents](https://mlsanity.com/paper/2605.08964/) (2026)

## Abstract (arXiv)

Individual probabilities refer to the probabilities of outcomes that are realized only once: the probability that it will rain tomorrow, the probability that Alice will die within the next 12 months, the probability that Bob will be arrested for a violent crime in the next 18 months, etc. Individual probabilities are fundamentally unknowable. Nevertheless, we show that two parties who agree on the data -- or on how to sample from a data distribution -- cannot agree to disagree on how to model individual probabilities. This is because any two models of individual probabilities that substantially disagree can together be used to empirically falsify and improve at least one of the two models. This can be efficiently iterated in a process of "reconciliation" that results in models that both parties agree are superior to the models they started with, and which themselves (almost) agree on the forecasts of individual probabilities (almost) everywhere. We conclude that although individual probabilities are unknowable, they are contestable via a computationally and data efficient process that must lead to agreement. Thus we cannot find ourselves in a situation in which we have two equally accurate and unimprovable models that disagree substantially in their predictions -- providing an answer to what is sometimes called the predictive or model multiplicity problem.