@inproceedings{kim-etal-2026-agreement,
title = "Agreement Is Not Truth: Characterizing and Controlling Consistent-but-Wrong Reasoning in {LLM}s",
author = "Kim, Minje and
Lee, Keeheon and
Lee, Chi-Guhn",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.emnlp-main.631/",
pages = "14482--14521",
ISBN = "979-8-89176-459-0",
abstract = "Self-consistency treats agreement among sampled chains of thought as evidence that the answer is correct. We show that this reading fails predictably. Across 5 reasoning datasets and 5 generators, consistent-but-wrong (CBW) rates track the task rather than the generator, and the pattern holds across agreement thresholds and sample budgets. On StrategyQA, at least 15{\%} of answers are wrong at 90{\%} self-agreement. We prove that no procedure reading only the answer distribution can always separate a question whose majority is right from one whose majority is wrong. We propose Risk-Controlled Self-Consistency (RISC), which combines the majority ratio with a verifier signal and calibrates an acceptance threshold by Learn-then-Test. It certifies the risk target in domain at finite sample size, and accepts nothing when no threshold qualifies. Against self-consistency alone, pooled selective error falls 3.01pp at 0.50 coverage; per-task gains are mixed. At 0.9 coverage, a local generator with a lightweight verifier costs {\textasciitilde}9{\texttimes} less than an all-API baseline and shows no detectable selective-error gap on four of five datasets. It trails on MATH500. Higher agreement is not always higher accuracy. Calibration narrows the gap, but more sampling usually does not."
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<abstract>Self-consistency treats agreement among sampled chains of thought as evidence that the answer is correct. We show that this reading fails predictably. Across 5 reasoning datasets and 5 generators, consistent-but-wrong (CBW) rates track the task rather than the generator, and the pattern holds across agreement thresholds and sample budgets. On StrategyQA, at least 15% of answers are wrong at 90% self-agreement. We prove that no procedure reading only the answer distribution can always separate a question whose majority is right from one whose majority is wrong. We propose Risk-Controlled Self-Consistency (RISC), which combines the majority ratio with a verifier signal and calibrates an acceptance threshold by Learn-then-Test. It certifies the risk target in domain at finite sample size, and accepts nothing when no threshold qualifies. Against self-consistency alone, pooled selective error falls 3.01pp at 0.50 coverage; per-task gains are mixed. At 0.9 coverage, a local generator with a lightweight verifier costs ~9× less than an all-API baseline and shows no detectable selective-error gap on four of five datasets. It trails on MATH500. Higher agreement is not always higher accuracy. Calibration narrows the gap, but more sampling usually does not.</abstract>
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%0 Conference Proceedings
%T Agreement Is Not Truth: Characterizing and Controlling Consistent-but-Wrong Reasoning in LLMs
%A Kim, Minje
%A Lee, Keeheon
%A Lee, Chi-Guhn
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F kim-etal-2026-agreement
%X Self-consistency treats agreement among sampled chains of thought as evidence that the answer is correct. We show that this reading fails predictably. Across 5 reasoning datasets and 5 generators, consistent-but-wrong (CBW) rates track the task rather than the generator, and the pattern holds across agreement thresholds and sample budgets. On StrategyQA, at least 15% of answers are wrong at 90% self-agreement. We prove that no procedure reading only the answer distribution can always separate a question whose majority is right from one whose majority is wrong. We propose Risk-Controlled Self-Consistency (RISC), which combines the majority ratio with a verifier signal and calibrates an acceptance threshold by Learn-then-Test. It certifies the risk target in domain at finite sample size, and accepts nothing when no threshold qualifies. Against self-consistency alone, pooled selective error falls 3.01pp at 0.50 coverage; per-task gains are mixed. At 0.9 coverage, a local generator with a lightweight verifier costs ~9× less than an all-API baseline and shows no detectable selective-error gap on four of five datasets. It trails on MATH500. Higher agreement is not always higher accuracy. Calibration narrows the gap, but more sampling usually does not.
%U https://aclanthology.org/2026.emnlp-main.631/
%P 14482-14521
Markdown (Informal)
[Agreement Is Not Truth: Characterizing and Controlling Consistent-but-Wrong Reasoning in LLMs](https://aclanthology.org/2026.emnlp-main.631/) (Kim et al., EMNLP 2026)
ACL