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Reasoning Concentrates Errors, and Self-Consistency Never Notices

Asaad Althoubi

arXiv:2609.32035v1cs.AI

TL;DR

Agreement is often treated as evidence of correctness, yet comparisons across different models cannot isolate reasoning’s role. Using fixed-weight reasoning toggles and evaluations across benchmarks, the paper finds that reasoning concentrates errors, while confidence weighting does not improve on majority voting.

  • Problem

    Comparisons between reasoning and non-reasoning models vary in training and other factors, leaving reasoning’s specific role difficult to identify.

    Source: §1 · p. 2

  • Method

    The study toggles reasoning within identical Qwen3 weights and evaluates answer distributions across five benchmarks, alongside six other models.

    Source: §1 · p. 2, §3 · p. 3

  • Results

    Reasoning raises wrong-answer collision in all ten within-weight comparisons, while no confidence-weighted method beats majority voting across 280 combinations after correction.

    Source: §1 · p. 2

  • Takeaways & Limitations

    In these evaluations, confidence weighting does not repair majority voting’s limitations, and a signal’s direction can depend on the model’s reasoning mode.

    Source: §9 · p. 9

    Several per-cell bootstrap intervals are wide and include zero, so the inference is the cross-cell pattern rather than any individual cell.

    Source: §4 · p. 5

Abstract

from arXiv · show

Self-consistency assumes that independent samples disagree when a model is unsure, so agreement is evidence of correctness. Holding weights fixed and toggling only a reasoning mode, over five benchmarks and 74,944 samples, we show that reasoning concentrates a model's errors: the probability that two independently drawn wrong answers coincide rises in all ten dataset-scale comparisons (p = 0.00098), and in nine of nine after restricting both arms to the problems each gets wrong. Where the answer space is unbounded, reasoning cuts the distinct answers produced to 0.43-0.65 of the non-reasoning count; where it is bounded, both arms hold an identical option set and reasoning concentrates mass on it instead, which no positional prior can explain at fixed weights. The aggregate cost is smaller than the mechanism predicts, because reasoning also shrinks the set of problems where answer diversity can decide anything, in ten of ten cells and by 2.7x; normalized for available headroom, both arms convert a quarter of it in domain. Confidence weighting does not recover what is left. Across 280 method-dataset-model combinations on eight models and five benchmarks, not one beats plain majority voting after correction; weighted voting agrees with it on 98.5% of problem-method pairs and is right 56.3% of the time on the rest; and a signal's direction can invert within fixed weights, with answer log-probability predicting correctness when reasoning is off and error when it is on. A learned six-signal combination gains nothing out of domain. Confidence signals should be evaluated on decisions, not on discrimination.

1 INTRODUCTION

Agreement is commonly treated as evidence of correctness, but prior work challenges that assumption and comparisons across different models cannot isolate reasoning. This paper toggles reasoning within fixed weights and finds that it concentrates errors while confidence-weighted aggregation does not improve on majority voting.

1 INTRODUCTION

  • Reasoning models and non-reasoning models differ in several factors, so cross-model comparisons cannot identify reasoning’s contribution; a prior hosted-model toggle was ignored by the provider.The paper instead uses Qwen3 modes selected by a chat-template flag, holding model weights and other stated settings fixed.Source: §1 · p. 2
  • p = 0.00098: reasoning raises the probability that two independently sampled wrong answers coincide in all ten dataset–scale comparisons, and in nine of nine matched comparisons.On unbounded answer spaces it reduces distinct answers; on bounded spaces it concentrates mass over the same options, which a positional prior cannot explain at fixed weights.Source: §1 · p. 2
  • The aggregate voting cost is smaller than the mechanism suggests: reasoning shrinks the problems where answer diversity can matter by 2.7×, and both arms convert about a quarter of available headroom.The apparent threefold advantage for non-reasoning disappears after normalization for headroom.Source: §1 · p. 2
  • Across 280 method–dataset–model combinations, no confidence-weighted method beats plain majority voting after correction, and answer log-probability’s direction reverses between reasoning modes.Weighted voting changes the answer rarely; when it does, it is right 56.3% of the time.Source: §1 · p. 2
  • The paper does not claim a measurable self-consistency penalty at this scale, and its replacement measure is supporting rather than confirmatory.The authors also withdrew a threefold accuracy-gain result after headroom normalization.Source: §1 · p. 2

2 RELATIONSHIP TO PRIOR WORK

Prior studies document limits of agreement-based confidence, voting, and consistency detectors, but they leave the causes incompletely measured. This paper distinguishes its contribution as a controlled measurement of sampled final-answer distributions, including errors, and revisits how answer length relates to confidence.

2 RELATIONSHIP TO PRIOR WORK

  • Existing work reports that self-consistent errors can evade entropy detection, agreement can coexist with incorrect answers, and majority voting can reduce per-problem accuracy.Tan et al. (2025) report below-chance detection of self-consistent errors; Ding (2026) reports weak agreement–correctness correlations; Bahuguna (2026) finds majority-vote costs and failed gating signals.Source: §2 · pp. 2–3
  • Earlier studies leave a measurement gap: Saha et al. (2026) analyze diversity among correct truncated continuations, while this paper measures repeated final answers with weights fixed.The paper says this reaches the error population excluded by Saha et al. (2026) and the controlled comparison unavailable to Ding (2026) and Tan et al. (2025); Kumaran (2026) uses a same-weight toggle but one response per trial.Source: §2 · p. 3
  • Prior length research finds uncertainty measures can be length-confounded, and this paper disputes a generalization from reasoning-model trace length to confidence across answer formats.Vashurin et al. (2025) propose residual debiasing; Santilli et al. (2025) discuss length-biased correctness; Devic et al. (2026) report higher trace-length AUROC for reasoning models, while this paper attributes the variable pattern to answer format.Source: §2 · p. 3

3 SETUP

The study uses eight open-weight models, five benchmarks, repeated sampling, and a prespecified analysis protocol. Its paired Qwen3 modes isolate reasoning, while the other models and varied answer formats support transfer and comparison.

3 SETUP

  • Eight open-weight models span four families; the two Qwen3 pairs share parameters and training ingredients, differing only in whether a reasoning chain is generated.The other four models are included to test whether the paired-model findings are a Qwen3 artifact.Source: §3 · p. 3
  • Five benchmarks cover 1,171 problems across open-ended and multiple-choice formats, with MATH-500 used for fitting and the other four datasets for out-of-domain evaluation.Crossing answer format with domain is intended to let Section 4 separate their contributions.Source: §3 · p. 3
  • Each model answers every problem independently eight times; responses are exact-match graded after normalization, using numeric comparisons for mathematics and option-letter comparisons for multiple choice.The paper gives 74,944 total records and reports answer rate beside accuracy.Source: §3 · pp. 3–4
  • The study evaluates twelve model-output confidence signals across six families, alongside an external reward model as a paid baseline.Signals include probes, entropy, log-probability, trace length, agreement, and hedging; higher values are oriented to mean more likely correct.Source: §3 · p. 4
  • Confidence intervals use problem-level cluster bootstrap, and Holm–Bonferroni correction is applied once across the 280 combinations.Toggle claims use paired exact sign tests, while generalization across models uses an unpaired exact Mann–Whitney test.Source: §3 · p. 4

4 REASONING CONCENTRATES ERRORS

Within fixed weights, reasoning concentrates incorrect answers across dataset–scale comparisons, with the pattern persisting on matched problems and across different answer-space formats. The paper also tests cross-model generalization and identifies design controls and limits on cell-level inference.

4 REASONING CONCENTRATES ERRORS

  • Median ∆ = +0.133, with a range of +0.035 to +0.431: collision among wrong answers favors reasoning in all ten within-weight comparisons (p = 0.00098).The cells are not fully independent, and several per-cell bootstrap intervals include zero, so the inference is the pattern across cells rather than any individual cell.Source: §4 · pp. 4–5
  • Reasoning reduces distinct answers to 0.43–0.65 of the non-reasoning count on open-ended sets, while on bounded sets it concentrates mass over the same four or ten keys.Collision rises by +0.121 to +0.181 on bounded tasks; the answer-space size stays fixed, so the change is in how probability mass is distributed.Source: §4 · p. 5
  • The fixed-weight design holds parameter count, family, and training data constant within pairs, and a positional prior cannot explain different concentration over identical keys.The effect appears at both 8B and 32B; the paper also contrasts this toggle with work that extends a reasoning budget beyond its natural stopping point and measures entropy over all answers.Source: §4 · p. 5
  • Across eight models, MATH-500 separates all reasoning from non-reasoning models (16/16, p = 0.014), while GPQA-Diamond and MMLU-Pro show consistent but incomplete ordering (14/16 each, p = 0.057).The latter two comparisons are reported as descriptive support rather than confirmation.Source: §4 · p. 5
  • Nine of nine matched comparisons favor reasoning (p = 0.00195), with median ∆ = +0.124; AMC at 32B is excluded because only seven problems qualify in both arms.The matched analysis is treated as confirmatory; the unmatched median ∆ is +0.133.Source: §4 · p. 5

5 WHAT THE CONCENTRATION COSTS

Reasoning shrinks the danger zone where answer diversity can determine a vote, while concentrating errors within that zone; after normalizing for available headroom, the in-domain accuracy gains are nearly identical.

5 WHAT THE CONCENTRATION COSTS

  • 0.250 versus 0.249 of available headroom is converted into accuracy gain by reasoning and non-reasoning models in domain, respectively.The raw gains of +0.011 and +0.035 are not comparable because reasoning models have about a third of the headroom.Source: §5 · pp. 5–6
  • 10 of 10 dataset–scale cells have a smaller danger zone with reasoning, averaging 2.72× smaller than without reasoning.The danger zone is the fraction of problems with fewer than half of eight samples correct; the mean is 0.136 with reasoning versus 0.369 without.Source: §5 · p. 6, Figure 1 · p. 6
  • 0.098 of danger-zone problems are rescued by plurality voting for reasoning models, against 0.144 for non-reasoning models.The ordering holds in 13 of 16 model pairings, but the authors report this as consistent with the concentration account, not confirmatory, because reasoning models yield few qualifying problems.Source: §5 · p. 6
  • 98.5% of problem–method pairs produce the same answer under weighted and plain majority voting, and weighted voting is right 56.3% of the time when they differ.Across 280 combinations, no confidence-weighted method significantly improves on majority voting after Holm–Bonferroni correction.Source: §5 · pp. 6–7
  • The same-benchmark contrast extends Bahuguna’s result: the danger zone falls from 47.0% without reasoning to 33.9% with reasoning on Qwen3-8B.The comparison uses identical weights, reaching a contrast the earlier infrastructure could not test.Source: §5 · p. 7
  • The danger-zone result is measured at k = 8, so its magnitude is specific to that sampling budget.The study covers vote weighting, not confidence-based filtering of the k samples.Source: §5 · p. 7

6 WHAT THIS DOES TO CONFIDENCE SIGNALS

Within fixed weights, reasoning does not improve agreement-based confidence results; apparent multiple-choice limits are bounded by guessing, and the comparison requires similar answer rates.

6 WHAT THIS DOES TO CONFIDENCE SIGNALS

  • 0.918 versus 0.952 agreement AUROC at 8B in domain, and 0.805 versus 0.869 out of domain, favor non-thinking over reasoning; the same ordering holds at 32B.This is a within-weights effect, not a claim that the result survives between-model comparison.Source: §6 · p. 7
  • 0.605 agreement AUROC for Gemma-3-12B on GPQA-Diamond is below its 0.735 guessing ceiling, not evidence by itself of a broken signal.The ceiling accounts for lucky guesses in the cleaned four-option answer space.Source: §6 · p. 7
  • All ten dataset–scale cells answer at rates within a pre-set 2% tolerance, with every cell at or above 0.9287.The authors report these residual answer-rate differences cannot account for the cited collision gaps or danger-zone ratios.Source: §6 · p. 7

7 LENGTH, REVISITED

Length is a strong confidence signal, but its apparent performance depends on answer format and distribution; a grading exposure also bounds some multiple-choice results.

7 LENGTH, REVISITED

  • Unmappable responses are systematically longer and scored incorrect, inflating Gemma multiple-choice length AUROC and shrinking out-of-domain gaps, but not affecting open-ended results.The authors identify this as a bounded exposure whose direction is known.Source: §7 · p. 8
  • Length AUROC spans 0.838–0.929 on MATH-500, with reasoning and non-reasoning means nearly identical at 0.872 and 0.878.The strongest value belongs to Gemma-3-27B, which has had no reasoning post-training; the paper attributes the contrast with other studies to answer-format differences and length variation.Source: §7 · p. 8
  • 0.757–0.965 is the length AUROC range on open-ended mathematics, versus 0.521–0.798 on multiple choice.For Qwen3-8B on MATH-500, hedging-expression AUROC drops from 0.807 to 0.474 after residualizing on output length.Source: §7 · p. 8
  • Length degrades out of domain in all eight models by 0.079–0.220, making it the least portable measured signal.The comparison evaluates a signal fitted in domain on a benchmark it was not fitted on, distinct from within-distribution difficulty changes.Source: §7 · p. 8

8 SIGNAL VALIDITY DEPENDS ON THE MODEL

Confidence-signal validity varies with model and benchmark: answer-token log-probability can reverse direction within fixed weights, and a six-signal selector does not generalize its in-domain gains.

8 SIGNAL VALIDITY DEPENDS ON THE MODEL

  • At 8B, answer-token log-probability’s selector weight inverts from +0.129 without reasoning to −0.176 with reasoning.The paper claims the inversion at 8B only; at 32B the magnitude instead collapses from −0.379 to −0.080.Source: §8 · pp. 8–9
  • 0.389–0.803 is the answer-token entropy range within a single model depending on benchmark, while answer-distribution entropy has macro AUROC 0.828–0.879.The two entropy measures are computed over different quantities: answer tokens versus the sampled answer distribution.Source: §8 · p. 9
  • Five of six off-diagonal selector AUROCs fall between 0.806 and 0.864, but Gemma-3-to-Qwen3 transfer is 0.728.Calibration can degrade more sharply: Gemma-3-to-Olmo-3 ECE is 0.343 against 0.097 for Olmo-3’s own selector.Source: §8 · p. 9
  • −0.0003 is the six-signal selector’s mean gain on four benchmarks it was not fitted on, losing on five of eight models.Its pooled gain is +0.0118 when the fitted benchmark is included.Source: §8 · p. 9

9 CONCLUSIONS AND RECOMMENDATIONS

The paper concludes that reasoning concentrates errors while shrinking the problems where answer diversity matters, leaving aggregate self-consistency gains nearly unchanged. It recommends evaluating confidence signals through decisions and reporting controls that separate reasoning, answer format, and length.

9 CONCLUSIONS AND RECOMMENDATIONS

  • Reasoning concentrates errors and shrinks the set of problems where answer diversity matters, so the two effects roughly cancel in aggregate accuracy.Across 280 combinations, no confidence-weighted method beat plain majority voting after correction, and signal direction depended on the model.Source: §9 · p. 9
  • Compare reasoning modes with fixed weights, report collision alongside agreement, and evaluate signals on decisions while identifying their direction for each model.Also report answer rate, token budgets, truncation, length-only baselines, and guessing ceilings where relevant.Source: §9 · p. 9
  • Five of sixteen preregistered predictions did not hold, and one failure became a finding in the paper’s length analysis.The conclusions say the failed prediction concerned whether reasoning would couple differently to length.Source: §9 · p. 10
  • The supplementary release includes per-sample records and analysis materials sufficient to recompute the collision index, danger zone, rescue rate, and 280-combination comparison without a GPU.Prompts and completions are withheld because they reproduce benchmark items; stable hashes allow records to join against the original benchmarks.Source: REPRODUCIBILITY STATEMENT · p. 10

A MODELS AND DATASETS

  • The two Qwen3 pairs share parameters, tokenizer, pre-training corpus, and post-training recipe, differing only in whether they generate a reasoning chain.Olmo-3 is included partly because its open weights, training data, and intermediate checkpoints make contamination questions answerable for that family.Source: Table 2 · p. 12, A MODELS AND DATASETS · p. 12

B THE COLLISION INDEX: ROBUSTNESS CHECKS AND A RELATED MEASURE

The collision increase persists across paired comparisons and matched subsets, while a smaller danger zone offsets its downstream effect on aggregate accuracy. Raw gains require headroom normalization, and confidence-weighted voting rarely changes majority decisions.

B THE COLLISION INDEX: ROBUSTNESS CHECKS AND A RELATED MEASURE

  • 9 of 9 matched comparisons favor reasoning (p = 0.00195), with median Δ = +0.124 versus +0.133 unmatched; all 19 bootstrap point estimates are positive.The matched analysis is confirmatory; AMC at 32B is dropped because only seven problems qualify in both arms, below the preset minimum of ten.Source: Table 4 · p. 13, B THE COLLISION INDEX: ROBUSTNESS… · p. 13, Table 5 · p. 14
  • Error semantic entropy independently measures concentration over semantic error clusters; its “stably wrong” state corresponds to the high-collision regime here.That study uses the measure as a confidence signal, whereas this paper treats it as an outcome of the reasoning toggle.Source: B THE COLLISION INDEX: ROBUSTNESS… · p. 13
  • 10 of 10 paired comparisons show greater wrong-answer collision with reasoning (exact sign test p = 0.00098).The comparison toggles reasoning within fixed weights.Source: Figure 2 · p. 14

C THE INVALID COMPARISON, IN FULL

  • The apparent threefold self-consistency gain difference is an artifact of unequal headroom: both arms convert almost exactly a quarter of what is available.Out of domain, the raw gain ordering reverses; per dataset it splits three to two.Source: C THE INVALID COMPARISON, IN FULL · pp. 15–16

D THE DANGER ZONE, PER CELL

  • 10 of 10 danger-zone comparisons favor reasoning; the mean danger-zone fraction is 0.136 against 0.369, or 2.72× smaller.The danger zone counts problems where fewer than half the usable samples are correct.Source: Table 8 · p. 16
  • Within fixed weights, reasoning uses 4.5× the tokens at k = 1: 6,324 versus 1,405 on average.The paper draws no cost recommendation because the reasoning arm is also 0.10–0.15 more accurate at k = 1.Source: D THE DANGER ZONE, PER CELL · p. 16
  • Reasoning rescues 0.098 of minority-correct problems versus 0.144 for non-reasoning, but the estimate is underpowered because fewer such problems qualify.Reasoning models contribute 47–107 qualifying problems against 121–154; the authors say more hard-regime problems or a closer-accuracy model pair is needed.Source: D THE DANGER ZONE, PER CELL · p. 17
  • Weighted voting agrees with majority voting on 98.5% of problem–method pairs and is correct on 56.3% of the cases where it differs.The high concentration of identical decisions leaves too few discordant cases for many exact tests to move from p = 1.000.Source: Figure 3 · p. 17, D THE DANGER ZONE, PER CELL · p. 17

E AGREEMENT WITHIN PAIRS, AND THE GUESSING CEILING

Agreement AUROC stays below the guessing ceiling in all sixteen multiple-choice cells, and reasoning sits farther below its own ceiling in both pairs and datasets. The appendix also checks answer-rate parity and qualifies how the token budget affects the AIME comparisons.

E AGREEMENT WITHIN PAIRS, AND THE GUESSING CEILING

  • Table 11’s agreement AUROC is pooled within each weight-pair and split, with Δ defined as reasoning off minus reasoning on.All four rows have positive Δ, favoring reasoning off.Source: E AGREEMENT WITHIN PAIRS, AND THE… · p. 18, Table 11 · p. 18
  • The ceiling assumes a knows-or-guesses model, and partial knowledge lowers K, making the bound harder—not easier—to satisfy.The derivation treats K as the fraction of problems known and guesses uniformly on the remainder; a signal cannot distinguish lucky from unlucky guesses.Source: E AGREEMENT WITHIN PAIRS, AND THE… · pp. 18–19
  • 16/16 cells respect the guessing ceiling, and reasoning sits farther below its ceiling in both pairs on both multiple-choice datasets.On GPQA-Diamond, non-thinking beats thinking despite its lower ceiling: 0.927 against 0.876 at 32B and 0.902 against 0.838 at 8B.Source: E AGREEMENT WITHIN PAIRS, AND THE… · p. 19, Table 12 · p. 19
  • No cluster-bootstrap interval reaches the guessing ceiling in any of the sixteen cells.The tightest case is olmo large on GPQA-Diamond: interval upper end 0.850 against a ceiling of 0.895.Source: E AGREEMENT WITHIN PAIRS, AND THE… · p. 19, Table 12 · p. 19

F ANSWER RATES AND TRUNCATION

  • AIME truncation is higher for reasoning models, so their statistics use marginally fewer samples, while the largest collision effects cannot be manufactured by that gap.At 32B, truncation is 0.0792 against 0.0458; on MATH-500 it stays between 0.0008 and 0.0088, versus 0.0028–0.1139 on AIME.Source: F ANSWER RATES AND TRUNCATION · pp. 20–21
  • 10/10 paired cells meet the pre-set 2% answer-rate tolerance, with the largest divergence at −0.0194 on AIME at 32B.The comparison uses parseable answers; truncation counts generations stopped at the 32,768-token budget.Source: F ANSWER RATES AND TRUNCATION · p. 19, Table 14 · p. 21

G LENGTH: THE MUTUAL-BIAS ARGUMENT AND THE TRANSFER GAPS

The paper uses exact-match grading to limit length-related mutual bias, while identifying unmappable answers as a remaining route for that bias. It also reports that signal transfer varies by signal and model.

G LENGTH: THE MUTUAL-BIAS ARGUMENT AND THE TRANSFER GAPS

  • Exact-match grading uses normalized numeric answers or option letters, avoiding the length-sensitive correctness functions that can distort length-dependent confidence signals.The paper treats this as a property of its grading design, not a robustness check applied afterward.Source: G LENGTH: THE MUTUAL-BIAS ARGUMENT AND… · p. 21
  • Unmappable responses remain an exposure: they are longer, inflating multiple-choice length AUROC for Gemma and shrinking out-of-domain gaps, but cannot affect open-ended results.The reported point-biserial correlations are 0.475 for gemma small on MMLU-Pro and 0.280 for gemma large on GPQA-Diamond.Source: G LENGTH: THE MUTUAL-BIAS ARGUMENT AND… · p. 21
  • The highest in-domain length AUROC belongs to a model with no reasoning post-training, distinguishing that result from the decode-time Qwen3 toggle.The two Gemma-3 models have had no reasoning post-training; Qwen3 non-thinking arms share weights with reasoning models.Source: G LENGTH: THE MUTUAL-BIAS ARGUMENT AND… · p. 21, Table 15 · p. 22
  • Length is the only signal whose in-domain minus out-of-domain AUROC is positive for all eight models.Positive values denote degradation; Figure 5 plots the gap by signal and model.Source: G LENGTH: THE MUTUAL-BIAS ARGUMENT AND… · p. 21, Table 16 · p. 22
  • Rank-space residualization differs from the prior linear correction and can expose signals previously suppressed by their length correlation.Residualizing negative length on length gives 0.500; the raw probe moves from 0.466 to 0.510.Source: G LENGTH: THE MUTUAL-BIAS ARGUMENT AND… · p. 22

H SIGNAL INSTABILITY ACROSS MODELS AND DATASETS

Signal behavior changes across models and datasets, and a learned combination does not improve on agreement counting out of domain. The appendix further reports cross-family transfer and pre-registered prediction outcomes.

H SIGNAL INSTABILITY ACROSS MODELS AND DATASETS

  • 0.389 to 0.803 is the range of olmo large’s mean answer-token entropy AUROC across MATH-500 and AIME, respectively.The in-domain above-chance split by family does not persist pooled across all five datasets; only Gemma-3 remains below chance.Source: H SIGNAL INSTABILITY ACROSS MODELS AND… · p. 22, Table 17 · p. 23
  • Figure 5 shows length is the only signal whose in-domain minus out-of-domain AUROC degrades across all eight models.The figure plots the gap by signal and model.Source: Figure 5 · p. 23
  • Across-family AUROC mostly transfers, but calibration can degrade sharply: Gemma-3-fitted, Olmo-3-evaluated ECE is 0.343 against Olmo’s 0.097.Five of six off-diagonal AUROCs are 0.806–0.864, compared with diagonal values of 0.819–0.870.Source: Table 18 · p. 24
  • A six-signal selector gains −0.0003 over raw agreement on the four benchmarks it was not fitted on and loses on five of eight models.Its pooled five-dataset advantage includes the fitted benchmark; the out-of-domain comparison does not.Source: H SIGNAL INSTABILITY ACROSS MODELS AND… · p. 23, Table 20 · p. 25

I PRE-REGISTERED PREDICTION SCORECARD

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