# When Does Delegation Beat Majority? A Delegation-Based Aggregator for Multi-Sample LLM Inference

arXiv: https://arxiv.org/abs/2606.08098 · HTML: https://mlsanity.com/paper/2606.08098/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 46 references that are in the map.
- First posted on arXiv 6 Jun 2026.

## Builds on (most cited first, 30 of 38)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Mixture-of-Agents Enhances Large Language Model Capabilities](https://mlsanity.com/paper/2406.04692/) (2024)
- [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)
- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [Universal Self-Consistency for Large Language Model Generation](https://mlsanity.com/paper/2311.17311/) (2023)
- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)
- [Let's Sample Step by Step: Adaptive-Consistency for Efficient Reasoning and Coding with LLMs](https://mlsanity.com/paper/2305.11860/) (2023)
- [Reasoning Aware Self-Consistency: Leveraging Reasoning Paths for Efficient LLM Sampling](https://mlsanity.com/paper/2408.17017/) (2024)
- [Beyond Semantic Entropy: Boosting LLM Uncertainty Quantification with Pairwise Semantic Similarity](https://mlsanity.com/paper/2506.00245/) (2025)
- [Beyond Majority Voting: LLM Aggregation by Leveraging Higher-Order Information](https://mlsanity.com/paper/2510.01499/) (2025)
- [Ranked Voting based Self-Consistency of Large Language Models](https://mlsanity.com/paper/2505.10772/) (2025)
- [Language Model Council: Democratically Benchmarking Foundation Models on Highly Subjective Tasks](https://mlsanity.com/paper/2406.08598/) (2024)
- [Certified Self-Consistency: Statistical Guarantees and Test-Time Training for Reliable Reasoning in LLMs](https://mlsanity.com/paper/2510.17472/) (2025)
- [The Sequential Edge: Inverse-Entropy Voting Beats Parallel Self-Consistency at Matched Compute](https://mlsanity.com/paper/2511.02309/) (2025)
- [Graph-based Confidence Calibration for Large Language Models](https://mlsanity.com/paper/2411.02454/) (2024)
- [On Rational Delegations in Liquid Democracy](https://mlsanity.com/paper/1802.08020/) (2018)
- [Know When You're Wrong: Aligning Confidence with Correctness for LLM Error Detection](https://mlsanity.com/paper/2603.06604/) (2026)

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

- [Uncertainty Quantification for LLM Agents: A Taxonomy, an Evaluation Protocol, and an Empirical Study](https://mlsanity.com/paper/2609.07395/) (2026)

## Abstract (arXiv)

Majority voting is the default unsupervised aggregator for multi-sample LLM inference, but it discards two signals: within-group answer entropy and between-group reasoning geometry. We aggregate by delegation instead (Propagational Proxy Voting, PPV): each group of samples keeps weight on its own answer in proportion to its entropy-based confidence (When) and routes the rest to peers by reasoning-embedding similarity (Whom); the stationary distribution of the resulting delegation matrix picks the consensus answer. This requires neither gold labels nor training. On MMLU-Pro with 128 samples per question, delegation beats majority by +1.5 pp overall and +2.24 pp on non-trivial questions (McNemar p ~ 1.0e-14, n = 8,099), overturning wrong majorities whose answer cluster is geometrically incoherent while the correct minority is tight. We then characterize exactly when delegation overturns majority: a two-option model gives a closed-form flip condition on each option's confidence and the weight it routes to the other, with a do-no-harm corollary for near-unanimous questions. The condition calls the realized winner on 96.5% of non-trivial questions, and its predicted mass gap tracks the realized gap at r = 0.97. We did not find any other unsupervised ensemble methods that close the oracle gap.