# A latent dimension of Condorcet's jury theorem for multiple AI advisers

arXiv: https://arxiv.org/abs/2609.14438 · HTML: https://mlsanity.com/paper/2609.14438/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 24 of its 66 references that are in the map.
- First posted on arXiv 13 Sep 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 24 of 24)

- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Replacing Judges with Juries: Evaluating LLM Generations with a Panel of Diverse Models](https://mlsanity.com/paper/2404.18796/) (2024)
- [ReConcile: Round-Table Conference Improves Reasoning via Consensus among Diverse LLMs](https://mlsanity.com/paper/2309.13007/) (2023)
- [Effect of Confidence and Explanation on Accuracy and Trust Calibration in AI-Assisted Decision Making](https://mlsanity.com/paper/2001.02114/) (2020)
- [Predictive Multiplicity in Classification](https://mlsanity.com/paper/1909.06677/) (2019)
- [Factuality Challenges in the Era of Large Language Models](https://mlsanity.com/paper/2310.05189/) (2023)
- [What Large Language Models Know and What People Think They Know](https://mlsanity.com/paper/2401.13835/) (2024)
- [Algorithmic Monoculture and Social Welfare](https://mlsanity.com/paper/2101.05853/) (2021)
- [Appropriate Reliance on AI Advice: Conceptualization and the Effect of Explanations](https://mlsanity.com/paper/2302.02187/) (2023)
- [Predictive Multiplicity in Probabilistic Classification](https://mlsanity.com/paper/2206.01131/) (2022)
- [Arbitrariness and Social Prediction: The Confounding Role of Variance in Fair Classification](https://mlsanity.com/paper/2301.11562/) (2023)
- [Nine Judges, Two Effective Votes: Correlated Errors Undermine LLM Evaluation Panels](https://mlsanity.com/paper/2605.29800/) (2026)
- [Does More Advice Help? The Effects of Second Opinions in AI-Assisted Decision Making](https://mlsanity.com/paper/2401.07058/) (2024)
- [Are Diversity Metrics Measuring Diversity? A Capability-Controlled Audit of Majority-Vote Gain in LLM Ensembles](https://mlsanity.com/paper/2607.20768/) (2026)
- [When Is Collective Intelligence a Lottery? Multi-Agent Scaling Laws for Memetic Drift in LLMs](https://mlsanity.com/paper/2603.24676/) (2026)
- [Benchmark Illusion: Disagreement among LLMs and Its Scientific Consequences](https://mlsanity.com/paper/2602.11898/) (2026)
- [DiscoUQ: Structured Disagreement Analysis for Uncertainty Quantification in LLM Agent Ensembles](https://mlsanity.com/paper/2603.20975/) (2026)
- [Not Just RLHF: Why Alignment Alone Won't Fix Multi-Agent Sycophancy](https://mlsanity.com/paper/2605.12991/) (2026)
- [LLMs as a Jury: Cross-Model Consensus Can Outperform Process Reward Models for LLM Reasoning](https://mlsanity.com/paper/2607.10139/) (2026)
- [Epistemic Filtering and Collective Hallucination: A Jury Theorem for Confidence-Calibrated Agents](https://mlsanity.com/paper/2602.22413/) (2026)
- [More Isn't Always Better: Balancing Decision Accuracy and Conformity Pressures in Multi-AI Advice](https://mlsanity.com/paper/2603.22152/) (2026)

## Abstract (arXiv)

When the same question is asked of multiple AI advisers, as in self-consistency and LLM-as-a-judge panels, Condorcet's jury theorem predicts that adding independent, competent advisers makes the majority more reliable. The theorem, however, has a latent dimension when viewed from the user's vantage: adding advisers also makes disagreement more visible. A binomial model reveals that this ``visible dissent'' becomes nearly inevitable as the number of advisers grows, and that reliability and disagreement approach certainty at rates that cross at an adviser accuracy of 4/5 (0.8); below it, visible dissent eventually becomes more likely than a correct majority. Even ideal panels of independent and competent advisers can be correct in aggregate but appear divided; such disagreement does not by itself indicate aggregation failure. The way advisers split also provides a common basis for predictive multiplicity, reconciliation load, and reliance miscalibration. These results separate aggregation from disclosure and turn the latter into testable questions about how disagreement should be presented and interpreted.