# When Can Voting Help, Hurt, or Change Course? Exact Structure of Binary Test-Time Aggregation

arXiv: https://arxiv.org/abs/2605.05592 · HTML: https://mlsanity.com/paper/2605.05592/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 30 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 21 of 21)

- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models](https://mlsanity.com/paper/2305.19187/) (2023)
- [Debating with More Persuasive LLMs Leads to More Truthful Answers](https://mlsanity.com/paper/2402.06782/) (2024)
- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)
- [Uncertainty Quantification and Deep Ensembles](https://mlsanity.com/paper/2007.08792/) (2020)
- [Confidence Improves Self-Consistency in LLMs](https://mlsanity.com/paper/2502.06233/) (2025)
- [Benchmarking Uncertainty Quantification Methods for Large Language Models with LM-Polygraph](https://mlsanity.com/paper/2406.15627/) (2024)
- [Uncertainty Baselines: Benchmarks for Uncertainty & Robustness in Deep Learning](https://mlsanity.com/paper/2106.04015/) (2021)
- [ConU: Conformal Uncertainty in Large Language Models with Correctness Coverage Guarantees](https://mlsanity.com/paper/2407.00499/) (2024)
- [Self-regularizing Property of Nonparametric Maximum Likelihood Estimator in Mixture Models](https://mlsanity.com/paper/2008.08244/) (2020)
- [Maximum Likelihood Estimation for Learning Populations of Parameters](https://mlsanity.com/paper/1902.04553/) (2019)
- [The Consistency Hypothesis in Uncertainty Quantification for Large Language Models](https://mlsanity.com/paper/2506.21849/) (2025)
- [On Efficient and Scalable Computation of the Nonparametric Maximum Likelihood Estimator in Mixture Models](https://mlsanity.com/paper/2208.07514/) (2022)
- [Two Calls, Two Moments, and the Vote-Accuracy Curve of Repeated LLM Inference](https://mlsanity.com/paper/2605.03379/) (2026)

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

- [Partially Correlated Verifier Cascades in LLM Harnesses: Concave Log-Odds, Polynomial Reliability, and Blind-Spot Ceilings](https://mlsanity.com/paper/2607.13918/) (2026)

## Abstract (arXiv)

Increasing a voting budget can improve or reduce population accuracy, and an initial gain or loss need not persist. We give a complete structural classification of these curves for binary unweighted majority under infinitely exchangeable correctness indicators, with an arbitrary latent success-probability law Pi. The classification is encoded by the signed voting signature  ω_Pi(B)=int 1q(1-q)∈ B(2q-1),Pi(,d q).  The complete odd-budget curve and this signature determine each other: the initial accuracy gives its total signed mass, and successive budget increments give its higher moments. Reflection-symmetric differences between latent laws are exactly the changes invisible to voting. A weighted total-variation constraint characterizes every attainable signature, and a minimum-mass allocation to the two reflected branches, completed by symmetric probability mass, gives every population producing its curve. Consequently, the full curve identifies the latent population precisely when no symmetric mass remains to redistribute.