# Stability of Weighted Majority Voting under Estimated Weights

arXiv: https://arxiv.org/abs/2207.06118 · HTML: https://mlsanity.com/paper/2207.06118/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 69 references that are in the map.
- First posted on arXiv 13 Jul 2022.

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

- [Who Said What: Modeling Individual Labelers Improves Classification](https://mlsanity.com/paper/1703.08774/) (2017)
- [Spectral Methods meet EM: A Provably Optimal Algorithm for Crowdsourcing](https://mlsanity.com/paper/1406.3824/) (2014)
- [Risk Bounds for the Majority Vote: From a PAC-Bayesian Analysis to a Learning Algorithm](https://mlsanity.com/paper/1503.08329/) (2015)
- [Error Rate Bounds and Iterative Weighted Majority Voting for Crowdsourcing](https://mlsanity.com/paper/1411.4086/) (2014)
- [Knowledge-Based Trust: Estimating the Trustworthiness of Web Sources](https://mlsanity.com/paper/1502.03519/) (2015)
- [Chebyshev-Cantelli PAC-Bayes-Bennett Inequality for the Weighted Majority Vote](https://mlsanity.com/paper/2106.13624/) (2021)
- [Consistency of weighted majority votes](https://mlsanity.com/paper/1312.0451/) (2013)
- [Exact Exponent in Optimal Rates for Crowdsourcing](https://mlsanity.com/paper/1605.07696/) (2016)
- [SLiMFast: Guaranteed Results for Data Fusion and Source Reliability](https://mlsanity.com/paper/1512.06474/) (2015)
- [Streaming Bayesian Inference for Crowdsourced Classification](https://mlsanity.com/paper/1911.05712/) (2019)
- [Frustratingly Easy Truth Discovery](https://mlsanity.com/paper/1905.00629/) (2019)

## Built on by (most cited first, 1 of 1)

- [Wound3DAssist: A Practical Framework for 3D Wound Assessment](https://mlsanity.com/paper/2508.17635/) (2025)

## Abstract (arXiv)

Weighted Majority Voting (WMV) is a well-known optimal decision rule for collective decision making, given the probability of sources to provide accurate information (trustworthiness). However, in reality, the trustworthiness is not a known quantity to the decision maker - they have to rely on an estimate called trust. A (machine learning) algorithm that computes trust is called unbiased when it has the property that it does not systematically overestimate or underestimate the trustworthiness. To formally analyse the uncertainty to the decision process, we introduce and analyse two important properties of such unbiased trust values: stability of correctness and stability of optimality. Stability of correctness means that the decision accuracy that the decision maker believes they achieved is equal to the actual accuracy. We prove stability of correctness holds. Stability of optimality means that the decisions made based on trust, are equally good as they would have been if they were based on trustworthiness. Stability of optimality does not hold. We analyse the difference between the two, and bounds thereon. We also present an overview of how sensitive decision correctness is to changes in trust and trustworthiness.