# Compare to Correct: Pairwise-Guided Logit Adjustment for LLM Test-Time Scaling

arXiv: https://arxiv.org/abs/2610.18583 · HTML: https://mlsanity.com/paper/2610.18583/

## 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 34 of its 47 references that are in the map.
- First posted on arXiv 13 Oct 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 34)

- [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)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [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)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [Long-tail learning via logit adjustment](https://mlsanity.com/paper/2007.07314/) (2020)
- [Towards a Human-like Open-Domain Chatbot](https://mlsanity.com/paper/2001.09977/) (2020)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [Universal Self-Consistency for Large Language Model Generation](https://mlsanity.com/paper/2311.17311/) (2023)
- [Scalable Best-of-N Selection for Large Language Models via Self-Certainty](https://mlsanity.com/paper/2502.18581/) (2025)
- [InternLM-Math: Open Math Large Language Models Toward Verifiable Reasoning](https://mlsanity.com/paper/2402.06332/) (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)
- [Escape Sky-high Cost: Early-stopping Self-Consistency for Multi-step Reasoning](https://mlsanity.com/paper/2401.10480/) (2024)
- [MathOdyssey: Benchmarking Mathematical Problem-Solving Skills in Large Language Models Using Odyssey Math Data](https://mlsanity.com/paper/2406.18321/) (2024)
- [Inference-Time Scaling for Complex Tasks: Where We Stand and What Lies Ahead](https://mlsanity.com/paper/2504.00294/) (2025)
- [Ranked Voting based Self-Consistency of Large Language Models](https://mlsanity.com/paper/2505.10772/) (2025)
- [A Theoretical Study on Bridging Internal Probability and Self-Consistency for LLM Reasoning](https://mlsanity.com/paper/2510.15444/) (2025)
- [Reliability-Aware Adaptive Self-Consistency for Efficient Sampling in LLM Reasoning](https://mlsanity.com/paper/2601.02970/) (2026)
- [PiCSAR: Probabilistic Confidence Selection And Ranking for Reasoning Chains](https://mlsanity.com/paper/2508.21787/) (2025)

## Abstract (arXiv)

Sampling-based test-time scaling enhances LLM reasoning by aggregating multiple reasoning paths for the same query. Existing methods use answer frequencies or path confidence to compute candidate scores, which do not explicitly characterize comparisons between competing answers. Inspired by the Condorcet principle in social choice theory, we introduce pairwise confidence comparisons between paths supporting different answers to capture answer-level comparative advantage. We combine this comparative evidence with voting support through a KL-regularized objective. Theoretically, we show that this comparative-advantage is equivalent to the adjustment to the traditional voting logits. In this way, our proposed Pairwise-Guided Logit Adjustment (PGLA) framework allows comparative evidence to compensate for weaker voting support and correct voting-based ranking errors. Experiments on 10 challenging benchmarks including mathematical reasoning, knowledge reasoning, and code generation with 7 models ranging from 1.7B to 32B parameters speak to the effectiveness of this plug-and-play term. Additional evaluations with external reward scores and online sampling further demonstrate its applicability.