Nudgeability: Reasoning Models Follow Confidence Signals Without Tracking Their Own Competence

Rohit Saxena; Utkarsh Upadhyay

cs.AISep 28, 2026

Nudgeability: Reasoning Models Follow Confidence Signals Without Tracking Their Own Competence

Authors: Rohit Saxena, Utkarsh Upadhyay

Abstract

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.

Figures & tables

Open-weight models ( $n=1000$ )
	MuSiQue 2-hop			StrategyQA
Model	$S$ (pp)	WT (%)	$L$ (pp)	$S$ (pp)	WT (%)	$L$ (pp)
Qwen3-4B	14.0	58.2	18.8 †	22.2	42.3	1.4
Qwen3-8B	22.4	42.5	1.9	19.0	39.5	3.8 †
Qwen3-14B	31.0	41.7	5.2 †	33.9	49.2	2.9
Qwen3-32B	38.3	37.2	6.8 †	38.3	54.7	1.7

Table 1: Confidence–doubt delegation swing (

S

), well-targeted flip share (

\mathrm{WT}

), and targeting lift (

L

) across both datasets. Nominal

n=1000

for open-weight models and

n=250

for provider-served models. Point estimates are reported here; † marks a lift whose 95% problem-bootstrap interval excludes zero, and the median row is taken per task over the nine open-weight models. Full 95% pointwise problem-bootstrap intervals, retained sample sizes (

n_{S}/n_{\mathrm{WT}}

), flip event counts (H/F), and random baselines appear in Appendix G.1 .

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Open-weight models
	MuSiQue 2-hop		StrategyQA
Model	correct/known	Acc. (%)	correct/known	Acc. (%)
Qwen3-4B	521/889	58.6	711/991	71.7
Qwen3-8B	597/939	63.6	763/999	76.4
Qwen3-14B	625/990	63.1	757/999	75.8
Qwen3-32B	658/992	66.3	816/1000	81.6

Appendix

Table 2: Unaided accuracy of the no-tool base,

P(s=1)

: correct answers over non-truncated no-tool generations (truncated generations have unknown competence and are excluded). Nominal

n=1000

for open-weight models and

n=250

for provider-served models.

Open-weight models ( $n=1000$ )
Task	Model	$n_{S}/n_{\mathrm{WT}}$	$S$ [CI]	H/F	WT [CI]	$\mathrm{WT}_{\mathrm{rand}}$ [CI]	Lift [CI]
MuSiQue	Qwen3-4B	966/876	14.0 [11.8, 16.3]	78/134	58.2 [49.2, 67.2]	39.4 [35.7, 43.1]	18.8 [10.7, 27.1]
MuSiQue	Qwen3-8B	944/921	22.4 [19.6, 25.1]	128/301	42.5 [36.4, 48.8]	40.6 [37.1, 44.1]	1.9 [-3.1, 7.1]
MuSiQue	Qwen3-14B	990/986	31.0 [28.0, 34.0]	134/321	41.7 [36.4, 47.1]	36.5 [33.5, 39.6]	5.2 [0.9, 9.6]
MuSiQue	Qwen3-32B	975/981	38.3 [35.1, 41.3]	136/366	37.2 [32.1, 42.2]	30.4 [27.4, 33.3]	6.8 [3.0, 10.7]
MuSiQue	Gemma4-E2B	1000/993	24.2 [21.5, 27.0]	108/293	36.9 [31.1, 42.9]	44.7 [41.1, 48.3]	-7.9 [-12.6, -3.0]

Appendix

Table 3: Confidence–doubt delegation swing (

S

), well-targeted flip share (

\mathrm{WT}

), random-selection reference (

\mathrm{WT}_{\mathrm{rand}}

), and targeting lift for every experiment, open continuation.

S

and lift are in percentage points; WT and

\mathrm{WT}_{\mathrm{rand}}

are percentages. H/F gives helpful/all flip events. Brackets are pointwise 95% problem-bootstrap intervals. Appendix G.1 describes the columns and retained populations.

Model	Task	$S_{0}$	$S_{1}$	$S_{2}$	$S_{3}$	$S_{\mathrm{pool}}$ [95% CI]
Qwen3-8B	StrategyQA	24.2	19.4	14.0	21.6	18.2 [13.1, 23.7]
Qwen3-8B	MuSiQue	21.4	17.5	11.2	15.5	14.7 [9.1, 20.6]
Gemma4-E4B	StrategyQA	24.2	18.6	21.3	22.7	20.8 [15.5, 26.3]
Gemma4-E4B	MuSiQue	70.0	40.4	45.1	43.5	43.0 [36.2, 49.8]
GLM-Z1-9B	StrategyQA	8.1	14.1	11.1	15.2	13.5 [9.1, 18.5]
GLM-Z1-9B	MuSiQue	3.4	5.0	6.0	1.0	4.0 [1.7, 6.7]

Appendix

Table 4: Stochastic-decoding sensitivity at temperature 1.0 and top-

p=0.95

S_{0}

is the greedy estimate;

S_{1}

–

S_{3}

are decode-seed estimates.

S_{\mathrm{pool}}

pools seed-paired problem contributions, and brackets give a 95% problem-clustered bootstrap interval. All values are percentage points.

		Unaided accuracy				WT
Model	Task	$0$	$1$	$2$	$3$	$0$	$1$	$2$	$3$	pool [95% CI]
Qwen3-8B	StrategyQA	72.0	74.0	75.0	75.0	52.2	32.1	43.5	29.6	34.6 [22.8, 47.9]
Qwen3-8B	MuSiQue	64.9	64.0	66.0	62.0	51.5	58.5	56.2	27.0	47.3 [35.9, 58.4]
Gemma4-E4B	StrategyQA	70.0	68.0	67.0	63.0	36.0	66.7	63.9	40.5	56.0 [44.9, 67.0]
Gemma4-E4B	MuSiQue	62.0	62.0	67.0	65.0	25.0	21.6	34.0	35.0	29.7 [20.4, 39.8]
GLM-Z1-9B	StrategyQA	72.7	71.4	68.0	70.7	50.0	68.8	26.3	60.0	50.0 [36.1, 64.1]

Appendix

Table 5: Unaided accuracy and well-targeted share under stochastic decoding (temperature 1.0, top-

p=0.95

, nominal

n=100

). Subscript 0 is the greedy run and 1–3 are decode seeds; each seed relabels competence from its own sampled no-tool answers.

\mathrm{WT}_{\mathrm{pool}}

pools seed-paired flip contributions, with a 95% problem-clustered bootstrap interval. All values are percent.

Task	Model	$n$	$B$	$\varnothing$	$\nu^{0}$	$\nu^{+}$	$\nu^{-}$
MuSiQue	Qwen3-4B	955	10.7	9.8	9.3	8.5	22.3
	Qwen3-8B	930	36.0	35.4	27.4	27.7	50.1
	Qwen3-14B	990	7.5	6.3	6.6	4.7	35.8
	Qwen3-32B	970	10.1	7.8	8.2	6.9	45.2
	Gemma4-E2B	1000	10.0	10.0	5.6	4.5	28.7
	Gemma4-E4B	1000	14.8	14.7	15.3	13.4	79.9

Appendix

Table 6: Delegation rate

P(A=\textsc{tool})

, in percent, for the uninterrupted with-tool base

B

and the four splice arms: sentence-less (

\varnothing

), neutral (

\nu^{0}

), confidence (

\nu^{+}

), and doubt (

\nu^{-}

). Nominal

n=1000

; each row’s arms share one pairwise-complete denominator

n

Task	Model	$D_{\mathrm{self}}$ (count)	$R_{\mathrm{self}}$ (count)
MuSiQue	Qwen3-4B	10.0 (49/489)	12.2 (38/312)
	Qwen3-8B	8.0 (33/411)	11.9 (21/177)
	Qwen3-14B	9.5 (56/587)	12.3 (39/316)
	Qwen3-32B	5.6 (34/607)	12.7 (32/251)
	Gemma4-E2B	21.0 (99/471)	11.1 (47/423)
	Gemma4-E4B	4.7 (25/527)	24.8 (54/218)

Appendix

Table 7: Supporting analysis at nominal

n=1000

. Correctness transitions when the tool-aware base still answers for itself. Rates are percentages.

D_{\mathrm{self}}

is correct-to-incorrect degradation and

R_{\mathrm{self}}

is incorrect-to-correct recovery; parentheses give numerator/eligible retained-self denominator.

Task	Model	First person	Expert	Task	Model	First person	Expert
MuSiQue	Qwen3-4B	14.0	2.7	StrategyQA	Qwen3-4B	22.2	15.6
	Qwen3-8B	22.4	12.8		Qwen3-8B	19.0	15.7
	Qwen3-14B	31.0	11.4		Qwen3-14B	33.9	47.9
	Qwen3-32B	38.3	13.8		Qwen3-32B	38.3	39.2
	Gemma4-E2B	24.2	10.3		Gemma4-E2B	7.3	2.4
	Gemma4-E4B	66.5	37.2		Gemma4-E4B	25.8	11.0

Appendix

Table 8: Supporting voice control at nominal

n=1000

: open-continuation swing by voice endpoint, in percentage points.

Task	Model	$\Phi$	$\rho$	$\omega$	Task	Model	$\Phi$	$\rho$	$\omega$
MuSiQue	Qwen3-4B	-1.2	90.0	39.6	StrategyQA	Qwen3-4B	-17.9	44.1	24.5
	Qwen3-8B	-1.8	64.3	29.0		Qwen3-8B	-2.8	22.7	18.9
	Qwen3-14B	+0.3	92.2	34.1		Qwen3-14B	-20.2	43.5	17.5
	Qwen3-32B	+2.0	87.9	29.4		Qwen3-32B	+0.2	18.9	11.1
	Gemma4-E2B	+6.5	83.5	45.1		Gemma4-E2B	-12.9	33.8	34.2
	Gemma4-E4B	+7.7	77.5	27.7		Gemma4-E4B	-7.5	41.8	20.5

Appendix

Table 9: Supporting oracle control at nominal

n=1000

: decomposition in percent/percentage points. Negative

\Phi

means the model delegates less to the generic free oracle than to the scoped tool.

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