# Strategic Self-Consistency

arXiv: https://arxiv.org/abs/2609.30352 · HTML: https://mlsanity.com/paper/2609.30352/

## 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 46 of its 49 references that are in the map.
- First posted on arXiv 24 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, 30 of 46)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [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)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [When More is Less: Understanding Chain-of-Thought Length in LLMs](https://mlsanity.com/paper/2502.07266/) (2025)
- [Tree Search for Language Model Agents](https://mlsanity.com/paper/2407.01476/) (2024)
- [Let's Sample Step by Step: Adaptive-Consistency for Efficient Reasoning and Coding with LLMs](https://mlsanity.com/paper/2305.11860/) (2023)
- [Confidence Improves Self-Consistency in LLMs](https://mlsanity.com/paper/2502.06233/) (2025)
- [Forest-of-Thought: Scaling Test-Time Compute for Enhancing LLM Reasoning](https://mlsanity.com/paper/2412.09078/) (2024)
- [Escape Sky-high Cost: Early-stopping Self-Consistency for Multi-step Reasoning](https://mlsanity.com/paper/2401.10480/) (2024)
- [Safe Testing](https://mlsanity.com/paper/1906.07801/) (2019)
- [Is Best-of-N the Best of Them? Coverage, Scaling, and Optimality in Inference-Time Alignment](https://mlsanity.com/paper/2503.21878/) (2025)
- [Inference-Aware Fine-Tuning for Best-of-N Sampling in Large Language Models](https://mlsanity.com/paper/2412.15287/) (2024)
- [Reasoning with Sampling: Your Base Model is Smarter Than You Think](https://mlsanity.com/paper/2510.14901/) (2025)
- [Hypothesis testing with e-values](https://mlsanity.com/paper/2410.23614/) (2024)
- [Make Every Penny Count: Difficulty-Adaptive Self-Consistency for Cost-Efficient Reasoning](https://mlsanity.com/paper/2408.13457/) (2024)
- [Reasoning Aware Self-Consistency: Leveraging Reasoning Paths for Efficient LLM Sampling](https://mlsanity.com/paper/2408.17017/) (2024)
- [zkLLM: Zero Knowledge Proofs for Large Language Models](https://mlsanity.com/paper/2404.16109/) (2024)
- [Are You Getting What You Pay For? Auditing Model Substitution in LLM APIs](https://mlsanity.com/paper/2504.04715/) (2025)
- [Retrain or not retrain: Conformal test martingales for change-point detection](https://mlsanity.com/paper/2102.10439/) (2021)
- [Auditing Black-Box LLM APIs with a Rank-Based Uniformity Test](https://mlsanity.com/paper/2506.06975/) (2025)
- [Fine-Tuning Games: Bargaining and Adaptation for General-Purpose Models](https://mlsanity.com/paper/2308.04399/) (2023)
- [CoIn: Counting the Invisible Reasoning Tokens in Commercial Opaque LLM APIs](https://mlsanity.com/paper/2505.13778/) (2025)
- [Competition and Diversity in Generative AI](https://mlsanity.com/paper/2412.08610/) (2024)
- [Is Your LLM Overcharging You? Tokenization, Transparency, and Incentives](https://mlsanity.com/paper/2505.21627/) (2025)
- [AuditLLM: A Tool for Auditing Large Language Models Using Multiprobe Approach](https://mlsanity.com/paper/2402.09334/) (2024)
- [Reliability-Aware Adaptive Self-Consistency for Efficient Sampling in LLM Reasoning](https://mlsanity.com/paper/2601.02970/) (2026)
- [AdaBoN: Adaptive Best-of-N Alignment](https://mlsanity.com/paper/2505.12050/) (2025)
- [Optimal Self-Consistency for Efficient Reasoning with Large Language Models](https://mlsanity.com/paper/2511.12309/) (2025)

## Abstract (arXiv)

Self-consistency has become a popular technique for enhancing the reasoning abilities of large language models by generating multiple reasoning paths and selecting the final answer through a majority vote. However, because model providers typically charge users in proportion to the number of reasoning paths generated, they have a financial incentive to artificially increase the path count. In this work, we show that an unfaithful provider can exploit this incentive using a simple, efficient algorithm while avoiding detection by an auditor: by generating and strategically reordering additional reasoning paths, the algorithm makes every path appear necessary to reach the majority. To validate our algorithm, we conduct experiments with multiple instruct models from the Llama and Qwen families, as well as reasoning models distilled from DeepSeek-R1, on benchmark datasets spanning mathematics, science, and question answering. Our results suggest that the distribution of additional reasoning paths generated by our algorithm is heavy-tailed and that substantial capacity to overcharge remains even under the best possible audit designed to keep the false-positive rate below α = 0.1.