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Nudgeability: Reasoning Models Follow Confidence Signals Without Tracking Their Own Competence
Rohit Saxena, Utkarsh Upadhyay
TL;DR
Tool-using reasoning models must decide when to answer unaided or delegate, and it is unclear whether reflective signals change that decision. The paper tests this with paired continuations that differ only by an inserted confidence or doubt sentence. Models respond strongly, but the resulting delegation changes are only weakly aligned with unaided competence.
Problem
Tool-using reasoning models must decide when to seek help, and a reflective mechanism must change behavior on the problems where help is needed.
Source: §1 · p. 1Method
A paired, post-training-free intervention inserts a first-person confidence or doubt sentence into an otherwise fixed reasoning trajectory and measures sensitivity and competence-based targeting.
Source: §1 · pp. 2–3Results
A median 20.6-percentage-point confidence-to-doubt swing accompanied a median 42% of induced flips being well-targeted, only +2 points over random selection.
Source: §6 · p. 9Takeaways & Limitations
Evaluating self-reflection requires measuring both whether a signal changes behavior and whether the resulting action matches unaided competence.
Source: §6 · p. 9The oracle condition is an upper bound rather than a deployable policy, and real routing must trade accuracy gains against latency, cost, privacy, and failure risk.
Source: §5 · p. 8
Abstract
from arXiv · showhide
Reasoning language models that can call tools must decide during inference whether to answer unaided or delegate. Any self-reflection mechanism for this must answer three questions: where the reflective signal comes from (verbal reports, output distributions, hidden states, a separate predictor), how it is presented to the model (numerical prediction, confidence token, prompt injection), and whether it changes the model's subsequent action. We isolate the third question. At a fixed point in otherwise identical reasoning trajectories, we insert a single first-person sentence expressing either confidence or doubt; the model then continues reasoning and chooses whether to answer directly or call a tool. Comparing these counterfactual continuations measures the causal effect of the reflective signal on delegation. We call this behavioral response Nudgeability and measure it along two dimensions: sensitivity, how strongly confidence and doubt change delegation rates, and targeting, whether delegation increases for problems the model cannot solve unaided and decreases for those it can. Across nine small-to-medium open-weight reasoning models from three families (Qwen, Gemma, and GLM) and two tasks, models are consistently sensitive: doubt increases delegation and confidence decreases it, with a median confidence-to-doubt swing of 20.6 percentage points, and 53 to 70 points for the larger provider-served models. This responsiveness is poorly targeted: a median 42% of induced flips are well-targeted, only a +2 percentage-point lift over a random-selection baseline. Confidence language is thus a strong control surface for delegation, but current models use it only weakly in accordance with their actual competence. Nudgeability offers a simple, post-training-free way to evaluate both sensitivity and targeting as endogenous self-reflection mechanisms mature.
1 Introduction
Tool-using reasoning models must decide when to delegate, but self-reflection involves distinct questions about a signal’s source, representation, and behavioral effect. This paper isolates behavioral effect by testing whether a supplied confidence or doubt sentence changes delegation within a fixed reasoning trajectory.
1 Introduction
- The paper separates reflection’s signal source, its representation to the model, and whether it changes the model’s subsequent behavior.An informative signal may be behaviorally inert, while an ungrounded statement may still steer a model.Source: §1 · pp. 2–3
- Paired continuations share the prompt and reasoning prefix; only the inserted first-person confidence or doubt sentence differs before the model chooses an answer or tool call.The model can continue reasoning after the sentence, so the paired delegation difference isolates its effect at that point in the trajectory.Source: §1 · p. 2
- Nudgeability separates sensitivity to a supplied signal from targeting: whether induced delegation changes align with demonstrated unaided competence.Targeting is measured by the fraction of competence-appropriate action changes and their lift over a random-selection baseline.Source: §1 · p. 2
- A median 20.6-percentage-point confidence-to-doubt swing showed strong sensitivity, but a median 42% of induced flips were well-targeted—only +2 points over random selection.Provider-hosted models showed swings of 53–70 points.Source: §1 · p. 3
2 Nudgeability Framework
The framework measures how confidence and doubt change delegation on paired continuations and whether induced action changes match a model’s observed unaided competence. It evaluates targeting against a matched random-selection baseline.
2 Nudgeability Framework
- Unaided correctness supplies the competence label: success calls for SELF, while failure calls for TOOL.Unknown or truncated unaided answers lack a competence label; this is a single-run operational measure, not latent ability under arbitrary resampling.Source: §2 · p. 4
- The paired splice appends a sentence to a fixed with-tool reasoning prefix and regenerates the continuation, with confidence, doubt, neutral, and sentence-less conditions.In the primary open-continuation condition, the model may reason after the splice; only the inserted sentence differs within a paired confidence–doubt comparison.Source: §2 · p. 4
- Sensitivity is the difference between doubt and confidence delegation rates on the same retained problems; positive values mean doubt shifts behavior toward tool use.Completed OTHER actions count as non-tool outcomes for this estimator.Source: §2 · p. 4
- Targeting counts competence-appropriate induced action flips, retaining both flip directions while excluding transitions involving OTHER.Each flip event counts separately, and the definition does not require the sentence polarity to match the flip direction or the tool call to succeed.Source: §2 · pp. 4–5
- Targeting lift compares competence-appropriate flips with random selection under the same action opportunities and flip volume.L = 0 indicates random-level targeting; L > 0 indicates flips favor problems where the new action matches unaided competence.Source: §2 · p. 5
3 Experimental Setup
The study evaluates open-weight and provider-served reasoning models on two verifiable question-answering tasks. The tasks contrast open-web fact finding with retrieval from supplied context.
3 Experimental Setup
- The primary cohort comprises nine open-weight models from Qwen3, Gemma4, and GLM-Z1, with DeepSeek-V4-Pro and MiniMax-M3 evaluated separately through provider APIs.Family, scale, and quantization are not factorially crossed, so comparisons among open-weight models are descriptive; provider-served model details are less auditable and the cohorts are not pooled.Source: §3 · p. 5
- The two tasks are StrategyQA, using scoped web search for implicit multi-step yes/no questions, and two-hop MuSiQue reading comprehension with supplied passages and a retrieval helper.The tasks contrast open-web fact finding with bounded retrieval from available context.Source: §3 · p. 5
- Each problem has an unaided and a tool-aware prompt; splice conditions reuse the with-tool reasoning prefix and leave the reasoning block open after insertion.Supporting free-perfect-oracle trials replace the scoped tool with ask_expert, described as returning a correct worked answer.Source: §3 · pp. 5–6
- Open-weight experiments use greedy decoding with nominal n = 1000 problems per model–task pair; provider-served experiments use n = 250.Sampled-decoding and repeated-label checks use n = 100, and retained counts vary by estimator.Source: §3 · p. 6
4 Results
Confidence and doubt reliably shift delegation, but the induced changes track unaided competence only weakly. This pattern holds across the evaluated model families and tasks, with sampled decoding preserving the direction of the effect.
4 Results
- 20.6 pp median confidence-to-doubt swing contrasts with a 42% median well-targeted flip share and only +2 pp targeting lift over random selection across open-weight experiments.Doubt increases tool use relative to confidence in every open-weight model–task experiment.Source: §4 · p. 6
- Doubt increases tool use across Qwen, Gemma, and GLM on both tasks; DeepSeek and MiniMax show the same direction, with provider-served swings exceeding 60 pp.The primary confidence–doubt contrast has the predicted sign in every open-weight model–task experiment.Source: §4 · p. 6
- Across three models, two tasks, and three decoding seeds, all 18 sampled-decoding swings remain positive and all six pooled intervals exclude zero.Sampling changes response magnitude, not its direction in this subset.Source: §4 · p. 6
- Most induced flips are SELF →TOOL transitions: 72% pooled and a majority in 17 of 18 open-weight experiments.Large sensitivity can coexist with weak or negative targeting lift.Source: §4 · p. 6
- 53–70 pp swings still yield lifts of −1.1 to +4.6 pp for Gemma4-E4B on MuSiQue and provider models, while Qwen3 on MuSiQue reaches +5.2 to +18.8 pp.GLM-Z1 responses are 3.7–10.1 pp; Gemma4-31B on MuSiQue is 1.3 pp at a 0.7% base delegation rate.Source: §4 · p. 6
- Targeting is task-dependent: L is positive in every StrategyQA experiment but negative in five of nine MuSiQue experiments, and S does not predict L (Spearman ρ = 0.13).The with-tool base delegates more on unaided failures than successes in 17 of 18 experiments, with median Γ = +5.6 pp; induced flips make little use of that signal.Source: §4 · pp. 6–7
- Even with a free, guaranteed-correct oracle, models answer directly on 19–96% of problems, with the spread driven mainly by task.Direct answering ranges from 64–96% on MuSiQue and mostly 19–44% on StrategyQA.Source: §4 · p. 7
- Cutting and regenerating without a sentence is nearly inert (median |∅−AB| = 0.3 pp), while first-person attribution moves delegation at least as much as expert attribution in 16 of 18 experiments.A neutral sentence is usually inert relative to ∅ (median −0.9 pp), but not always; sealing the think block keeps S > 0 in all 18 experiments while changing its magnitude.Source: §4 · pp. 7–8
5 Discussion and Limitations
Confidence language can reliably shift delegation without directing those shifts toward problems the model cannot solve unaided. Nudgeability therefore measures a control surface, not a useful delegation policy by itself.
5 Discussion and Limitations
- Consistent Nudgeability across model families, datasets, and sizes makes confidence language a potential control surface, but induced changes remain weakly concentrated on problems needing help.A model may delegate more when expressing doubt with little regard for whether it would actually fail the problem.Source: §5 · p. 8
- Evaluating delegation only by its effect on tool-use rates can miss wasted latency and cost on solvable problems or confident errors when delegation is suppressed.The paper recommends reporting sensitivity together with targeting lift.Source: §5 · p. 8
- A local-to-remote model router must trade expected accuracy gain against latency, monetary cost, privacy, and failure risk; the simulated oracle is an upper bound, not a deployable policy.Nudgeability tests whether a supplied signal changes action, while L assesses whether that change points toward cases needing help.Source: §5 · p. 8
- Reasoning-trace edits can influence later actions, but the results do not show that displayed traces faithfully represent internal computation or that natural confidence statements behave similarly.The authors motivate treating reasoning-channel interventions as part of behavioral and safety evaluation.Source: §5 · p. 8
- The intervention changes a later action but does not establish that executing the tool call improves the final answer, and the two evaluated QA tasks do not span deployed agents’ tool range.Family, scale, quantization, and serving stack are not factorially crossed, so apparent patterns across them are descriptive.Source: §5 · pp. 8–9
- A reflective mechanism needs a grounded uncertainty signal and a response that uses it selectively; future signals could be evaluated through the same intervention interface.The authors propose mapping output-based, semantic-entropy, hidden-state, or activation-level estimates into that interface.Source: §5 · pp. 8–9
6 Conclusion
A paired, post-training-free intervention tests whether confidence language changes tool delegation and whether those changes track unaided competence. Models respond reliably, but the induced changes are only weakly selective.
6 Conclusion
- 20.6 pp is the median confidence-to-doubt swing across open-weight experiments, while provider-served models show swings of 53–70 pp; only 42% of flips are well targeted, with +2 pp median lift over matched random selection.The results indicate reliable steering through confidence language but weak selectivity about where it applies.Source: §6 · p. 9
- Nudgeability separates sensitivity—whether a signal moves behavior—from targeting—whether it moves behavior on the right problems.The paper presents this as a simple test for future self-reflection mechanisms.Source: §6 · p. 9
- A practical reflective system needs uncertainty grounded in correctness and an action response that uses the signal selectively.Improving uncertainty production or representation alone is not sufficient.Source: §6 · p. 9
Reproducibility Statement
The reproducibility statement specifies sampling, decoding, estimators, and statistical procedures, and says the code will be released upon publication.
Reproducibility Statement
- Problems were sampled from MuSiQue and StrategyQA with a fixed seed, and all statistics were deterministic post-processing of the records.The statement points to Section 3 for sampling details and Appendices E and F for the bootstrap procedure.Source: Reproducibility Statement · p. 9
- Primary runs used greedy decoding; the sampled-decoding check used temperature 1.0, top-p = 0.95, and three decoding seeds.The sampled-decoding settings are specified in Appendix G.5.Source: Reproducibility Statement · p. 9
- The paper specifies models, prompts, decoding settings, and estimators, and states that code will be released upon publication.The exact splice prefixes and inserted sentences are in Appendix C; Figure 4 shows a complete prompt.Source: Reproducibility Statement · p. 9
AI Use Disclosure
The authors disclose using generative AI tools for manuscript preparation, related-work discovery, and research execution, with the authors reviewing assisted content and taking responsibility.
AI Use Disclosure
- Generative AI tools were used to polish and condense prose, draft and restructure manuscript sections, and prepare LaTeX for tables and figures.The tools named include Claude, OpenAI, DeepSeek, and GLM models.Source: AI Use Disclosure · p. 9
- AI tools were used to locate and summarize related work, and the authors checked every cited work against its original source.Source: AI Use Disclosure · p. 9
- AI tools assisted with implementing and debugging experiment code and data processing; the authors reviewed all assisted content and take full responsibility.Source: AI Use Disclosure · p. 9
A Related Work
The paper distinguishes finding or representing reflective signals from testing whether they change a model’s next action. Its paired evaluation asks how strongly confidence language steers delegation and whether those changes align with unaided competence.
Verbal reflection and uncertainty
- Prior work estimates correctness from verbal or probabilistic reports, sampled-answer diversity, or hidden representations; Nudgeability instead tests the response to a supplied signal.The cited approaches investigate where correctness information can be found and how accurately it can be recovered [Kadavath et al., 2022, Farquhar et al., 2024, Kossen et al., 2024, Ghasemabadi and Niu, 2025].Source: A Related Work · p. 12
Limits on introspective claims
- The experimenter supplies the confidence or doubt sentence, so its effect does not establish that the model extracted, estimated, or truthfully reported its own uncertainty.The study tests control through reflection-like language, not the signal’s provenance or faithfulness.Source: A Related Work · p. 12
Related work and contribution
- The study varies confidence language at a fixed reasoning-prefix boundary, measures delegation rather than answer content, and tests whether induced changes align with unaided competence.Its paired counterfactual design holds the problem and preceding trajectory fixed.Source: A Related Work · p. 12
Intervention and tool use
- Unlike work that changes reasoning traces or routing policies, this study intervenes on expressed confidence while evaluating a delegation decision inside the reasoning model.The paper describes routing-policy work as complementary: a controller may supply a signal, while Nudgeability measures whether the model changes delegation when it is presented.Source: A Related Work · pp. 12–13
Tool use and abstention
- Abstention defers an answer, whereas a tool call may continue the attempt by acquiring information or computation; both involve judging when an unaided answer should not be trusted.The targeting measure tests whether intervention-induced delegation rises on problems failed unaided and falls on problems solved unaided.Source: A Related Work · p. 13
B Control Experiments
The supporting experiments vary prompt components while keeping others fixed or inheriting them from a base run. The paper also specifies splice conditions and diagnostics that contextualize delegation and its targeting against a matched random-selection reference.
B Control Experiments
- The voice controls change who is credited with the confidence judgment, while the oracle and sealed conditions test tool-request difficulty and continuation-boundary effects.The oracle replaces the scoped tool with a free perfect oracle; the sealed condition inserts a think-close marker after the nudge, though this also changes the continuation boundary.Source: B Control Experiments · p. 13
C Intervention Anatomy
- A core splice combines the original with-tool prompt and stored reasoning text, then continues the assistant turn after inserting the intervention sentence.Neutral sentences and a sentence-less splice are separate controls; the latter tests cut-and-regeneration effects and differs from the uninterrupted base used to identify induced flips.Source: C Intervention Anatomy · pp. 14–15
D Supporting delegation diagnostics
- The free perfect-oracle controls measure residual self-reliance and conditional overconfidence when delegation is costless and guarantees a correct response.Conditional overconfidence is the fraction of retained self-answers on problems the model failed unaided, despite access to the guaranteed-correct option; these are supporting diagnostics, not primary Nudgeability measures.Source: D Supporting delegation diagnostics · p. 15
E Random-Selection Reference
- The matched reference preserves intervention arm, baseline action, eligible problem pool, and flip count, then selects which problems flip without using competence.It estimates expected helpful flips within strata as FνbKνb/Nνb; targeting lift compares observed targeting against this reference, not the downstream value of the tool.Source: E Random-Selection Reference · p. 16
- The random-reference procedure resamples whole problems and recomputes targeting and lift; its 95% percentile intervals are not randomization tests or multiplicity-adjusted superiority declarations.At fixed flip counts, high sensitivity can exhaust helpful opportunities even under selective allocation.Source: E Random-Selection Reference · p. 16
F Statistical Analysis
The statistical analysis pairs primary comparisons by problem and fixed reasoning prefix, using bootstrap intervals and a paired test for directional changes. A sampled-decoding check examines whether the greedy-decoding result’s direction is robust.
Statistical Analysis
- Primary comparisons are paired by problem and fixed reasoning prefix; sensitivity is reported in percentage points, targeting as a percentage with counts, and lift relative to the matched random-selection reference.Nonparametric bootstrap intervals use 20,000 problem-level replicates and are reported at 95%.Source: F Statistical Analysis · pp. 16–17
- McNemar’s test assesses directional changes in paired confidence–doubt tool indicators, while cross-model and cross-task medians summarize experiment-level estimates rather than pooled problem rows.Intervals quantify variation over sampled problems under the fixed model and decoding configuration, not variation across checkpoints, serving stacks, or decoding seeds.Source: F Statistical Analysis · p. 17
- A sampled-decoding sensitivity analysis repeats a fixed subset of three models on both tasks at temperature 1.0, top-p = 0.95, and three seeds to test directional robustness.The study pairs positive and negative arms within each seed and does not pool this analysis with the primary greedy campaign.Source: F Statistical Analysis · p. 17
G.1 Full Sensitivity and Targeting Results
The appendix reports primary sensitivity and targeting estimates, with provider-served models showing large delegation swings but little improvement over random targeting. Additional analyses test decoding variability, splice controls, sealed continuations, natural delegation, and supporting controls.
G.2 Provider-Served Models
- At n = 250, provider-served models show S of 53.0–70.0 pp, WT of 27.1%–47.7%, and targeting lift of −1.1 to +4.6 pp across four experiments.The MiniMax-M3 MuSiQue experiment had 244 splice continuations after six with-tool bases lacked usable completed reasoning segments.Source: §G.2 · p. 18
G.3 Flip composition; G.4 Problem-Sampling Uncertainty
- Figure 5 partitions flips by SELF→TOOL versus TOOL→SELF direction and by competence alignment; bootstrap intervals quantify problem-sampling uncertainty under fixed seeds and decoding configurations.The intervals do not quantify uncertainty across seeds, temperatures, or serving stacks.Source: §G.3 · p. 18, §G.4 · pp. 18–19, Figure 5 · p. 19
G.5 Sampled-Decoding Sensitivity
- All six stochastic-decoding experiments meet the directional criterion and have pooled intervals excluding zero, while targeting is less stable across seeds than sensitivity.Unaided accuracy varies by at most 7 pp across runs, whereas WT varies by 13–43 pp within an experiment; three seeds were selected for a directional stress test, not variance-component estimation.Source: §G.5 · pp. 19–20, Table 4 · p. 19, Table 5 · p. 19
G.6 Delegation Rates Across the Base and Splice Arms
- The neutral sentence is usually but not always inert: it shifts delegation by at least 3 pp in four of 18 experiments and lowers it by 31.4 pp for Qwen3-32B on StrategyQA.The sentence-less splice has a median absolute difference of 0.3 pp from the uninterrupted base, and the confidence–doubt contrast is therefore measured against each other rather than the neutral arm.Source: §G.6 · p. 20, Table 6 · p. 20
G.7 Sealed-Continuation Sanity Check
- Sealed continuations change the confidence–doubt swing by −20.8 to +53.7 pp relative to open continuations, with the direction varying across models.Sealing removes the opportunity to reason after the inserted statement and is treated as a sanity check, not pooled with the primary result.Source: §G.7 · p. 20
G.8 Natural Delegation and the Oracle Control
- Natural delegation has a positive targeting gap in 17 of 18 open-weight model–task experiments, while a free perfect oracle does not eliminate direct answers on problems failed unaided.Under the oracle, direct-answer rates range from 18.9% to 96.2%; on retained self-answers, 11.1%–45.1% occur on problems the model failed unaided.Source: §G.8 · p. 21
G.9 Retained Self-Answer Correctness
- Table 7 conditions correctness transitions on gradeable no-tool answers and with-tool bases that still choose SELF, so these rates are not estimates of delegation value.Adding the tool definition can change the generated continuation even when the final action remains SELF.Source: §G.9 · p. 21, Table 7 · p. 21
G.10 Supporting Control Details
- Expert attribution exceeds first-person attribution only for Qwen3-14B and Qwen3-32B on StrategyQA and the tied or near-tied GLM-Z1-9B MuSiQue experiment.In the remaining experiments, self-attribution is at least as strong.Source: §G.10 · p. 21, Table 8 · p. 22