# Selecting a number of voters for a voting ensemble

arXiv: https://arxiv.org/abs/2104.11833 · HTML: https://mlsanity.com/paper/2104.11833/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 58 references that are in the map.
- First posted on arXiv 23 Apr 2021.

## Builds on (most cited first, 4 of 4)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Less Is More: A Comprehensive Framework for the Number of Components of Ensemble Classifiers](https://mlsanity.com/paper/1709.02925/) (2017)
- [Hypothesis Testing for High-Dimensional Multinomials: A Selective Review](https://mlsanity.com/paper/1712.06120/) (2017)
- [A Simple Algorithm for Exact Multinomial Tests](https://mlsanity.com/paper/2008.12682/) (2020)

## Built on by (most cited first, 2 of 2)

- [Leveraging Linear Independence of Component Classifiers: Optimizing Size and Prediction Accuracy for Online Ensembles](https://mlsanity.com/paper/2308.14175/) (2023)
- [Ensemble Performance Through the Lens of Linear Independence of Classifier Votes in Data Streams](https://mlsanity.com/paper/2511.21465/) (2025)

## Abstract (arXiv)

For a voting ensemble that selects an odd-sized subset of the ensemble classifiers at random for each example, applies them to the example, and returns the majority vote, we show that any number of voters may minimize the error rate over an out-of-sample distribution. The optimal number of voters depends on the out-of-sample distribution of the number of classifiers in error. To select a number of voters to use, estimating that distribution then inferring error rates for numbers of voters gives lower-variance estimates than directly estimating those error rates.