# Truthful Calibration Measures for Sequential Prediction

arXiv: https://arxiv.org/abs/2608.21348 · HTML: https://mlsanity.com/paper/2608.21348/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 23 references that are in the map.
- First posted on arXiv 21 Aug 2026.

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

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [A Unifying Theory of Distance from Calibration](https://mlsanity.com/paper/2211.16886/) (2022)
- [Stronger Calibration Lower Bounds via Sidestepping](https://mlsanity.com/paper/2012.03454/) (2020)
- [Forecast Hedging and Calibration](https://mlsanity.com/paper/2210.07169/) (2022)
- [Breaking the T2/3 Barrier for Sequential Calibration](https://mlsanity.com/paper/2406.13668/) (2024)
- [Truthfulness of Decision-Theoretic Calibration Measures](https://mlsanity.com/paper/2503.02384/) (2025)
- [Smooth Calibration and Decision Making](https://mlsanity.com/paper/2504.15582/) (2025)
- [Truthfulness of Calibration Measures](https://mlsanity.com/paper/2407.13979/) (2024)
- [A Perfectly Truthful Calibration Measure](https://mlsanity.com/paper/2508.13100/) (2025)
- [Testable and Actionable Calibration for Full Swap Regret](https://mlsanity.com/paper/2605.17749/) (2026)
- [Truthful Calibration Errors for Multi-Class Prediction](https://mlsanity.com/paper/2510.06388/) (2025)

## Abstract (arXiv)

Calibration requires probabilistic reports to be conditionally unbiased and reliably interpretable as probabilities. A calibration measure assigns numerical error to miscalibrated reports. Haghtalab et al. (2024) proposed an approximately truthful calibration measure for online prediction, leaving open whether exact truthfulness is compatible with completeness and soundness. We resolve this question negatively for sequential binary prediction: exact truthfulness is incompatible with completeness and soundness, even for independent outcomes. We then show that this impossibility is specific to exact truthfulness. We give two general reductions from a base calibration measure, producing additively and multiplicatively approximately truthful calibration measures, respectively. Applying the multiplicative reduction, for every 0 < varepsilon < 1 we construct a sound and complete calibration measure that is (1+exp(-T(1-varepsilon)/2/2))-multiplicatively truthful. This improves the approximate-truthfulness guarantee of Haghtalab et al. (2024).