# The Scope of Multicalibration: Characterizing Multicalibration via Property Elicitation

arXiv: https://arxiv.org/abs/2302.08507 · HTML: https://mlsanity.com/paper/2302.08507/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 33 references that are in the map.
- First posted on arXiv 16 Feb 2023.

## Builds on (most cited first, 10 of 10)

- [Multiaccuracy: Black-Box Post-Processing for Fairness in Classification](https://mlsanity.com/paper/1805.12317/) (2018)
- [Outcome Indistinguishability](https://mlsanity.com/paper/2011.13426/) (2020)
- [Omnipredictors](https://mlsanity.com/paper/2109.05389/) (2021)
- [Batch Multivalid Conformal Prediction](https://mlsanity.com/paper/2209.15145/) (2022)
- [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)
- [Low-Degree Multicalibration](https://mlsanity.com/paper/2203.01255/) (2022)
- [Multicalibration as Boosting for Regression](https://mlsanity.com/paper/2301.13767/) (2023)
- [Online Minimax Multiobjective Optimization: Multicalibeating and Other Applications](https://mlsanity.com/paper/2108.03837/) (2021)

## Built on by (most cited first, 6 of 6)

- [Scalable Membership Inference Attacks via Quantile Regression](https://mlsanity.com/paper/2307.03694/) (2023)
- [Oracle Efficient Online Multicalibration and Omniprediction](https://mlsanity.com/paper/2307.08999/) (2023)
- [Generalized Venn and Venn-Abers Calibration with Applications in Conformal Prediction](https://mlsanity.com/paper/2502.05676/) (2025)
- [Orthogonal Causal Calibration](https://mlsanity.com/paper/2406.01933/) (2024)
- [Bellman Calibration for V-Learning in Offline Reinforcement Learning](https://mlsanity.com/paper/2512.23694/) (2025)
- [Bellman Calibration for Marginalized Importance Weighting in Offline Reinforcement Learning](https://mlsanity.com/paper/2608.24858/) (2026)

## Abstract (arXiv)

We make a connection between multicalibration and property elicitation and show that (under mild technical conditions) it is possible to produce a multicalibrated predictor for a continuous scalar distributional property Gamma if and only if Gamma is elicitable. On the negative side, we show that for non-elicitable continuous properties there exist simple data distributions on which even the true distributional predictor is not calibrated. On the positive side, for elicitable Gamma, we give simple canonical algorithms for the batch and the online adversarial setting, that learn a Gamma-multicalibrated predictor. This generalizes past work on multicalibrated means and quantiles, and in fact strengthens existing online quantile multicalibration results. To further counter-weigh our negative result, we show that if a property Gamma1 is not elicitable by itself, but is elicitable conditionally on another elicitable property Gamma0, then there is a canonical algorithm that jointly multicalibrates Gamma1 and Gamma0; this generalizes past work on mean-moment multicalibration. Finally, as applications of our theory, we provide novel algorithmic and impossibility results for fair (multicalibrated) risk assessment.