# Merging uncertainty sets via majority vote

arXiv: https://arxiv.org/abs/2401.09379 · HTML: https://mlsanity.com/paper/2401.09379/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2024.

## Built on by (most cited first, 30 of 30)

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- [Multi-model Online Conformal Prediction with Graph-Structured Feedback](https://mlsanity.com/paper/2506.20898/) (2025)
- [Uncertainty Quantification With Multiple Sources](https://mlsanity.com/paper/2405.06479/) (2024)
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- [Derandomizing Simultaneous Confidence Regions for Band-Limited Functions by Improved Norm Bounds and Majority-Voting Schemes](https://mlsanity.com/paper/2506.17764/) (2025)
- [CAOS: Conformal Aggregation of One-Shot Predictors](https://mlsanity.com/paper/2601.05219/) (2026)
- [Data-light Uncertainty Set Merging with Admissibility](https://mlsanity.com/paper/2410.12201/) (2024)
- [On the Precise Asymptotics of Universal Inference](https://mlsanity.com/paper/2503.14717/) (2025)
- [Improving Coverage in Combined Prediction Sets with Weighted p-values](https://mlsanity.com/paper/2505.11785/) (2025)
- [Class conditional conformal prediction for multiple inputs by p-value aggregation](https://mlsanity.com/paper/2507.07150/) (2025)
- [Enhanced Multi-model Online Conformal Prediction](https://mlsanity.com/paper/2601.01692/) (2026)
- [Conformalized Super Learner](https://mlsanity.com/paper/2604.22391/) (2026)
- [Set-Preserving Calibration from Conformal P-Values to E-Values](https://mlsanity.com/paper/2606.03600/) (2026)
- [Aggregation of Statistical Evidence under Exchangeability](https://mlsanity.com/paper/2607.15823/) (2026)
- [Beyond Point Predictions: Uncertainty-Aware Satellite Poverty Mapping for Public Policy](https://mlsanity.com/paper/2608.23322/) (2026)
- [Unifying Conformal Language Tasks with In-Context Ensembles](https://mlsanity.com/paper/2609.03005/) (2026)
- [Rolling Conformal Prediction in Sequential Model Training](https://mlsanity.com/paper/2609.26951/) (2026)
- [Byzantine-Robust Federated RAG via Aligned Calibration and Fixed-Membership Conformal Prediction](https://mlsanity.com/paper/2609.33037/) (2026)
- [Cross-Fitting Under Nonregularity: Normality and Inference via Locality](https://mlsanity.com/paper/2610.02944/) (2026)

## Abstract (arXiv)

Given K uncertainty sets that are arbitrarily dependent -- for example, confidence intervals for an unknown parameter obtained with K different estimators, or prediction sets obtained via conformal prediction based on K different algorithms on shared data -- we address the question of how to efficiently combine them in a black-box manner to produce a single uncertainty set. We present a simple and broadly applicable majority vote procedure that produces a merged set with nearly the same error guarantee as the input sets. We then extend this core idea in a few ways: we show that weighted averaging can be a powerful way to incorporate prior information, and a simple randomization trick produces strictly smaller merged sets without altering the coverage guarantee. Further improvements can be obtained if the sets are exchangeable. We also show that many modern methods, like split conformal prediction, median of means, HulC and cross-fitted ``double machine learning'', can be effectively derandomized using these ideas.