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

arXiv: https://arxiv.org/abs/2609.34572 · HTML: https://mlsanity.com/paper/2609.34572/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 22 of its 24 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 22 of 22)

- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [MuSiQue: Multihop Questions via Single-hop Question Composition](https://mlsanity.com/paper/2108.00573/) (2021)
- [Did Aristotle Use a Laptop? A Question Answering Benchmark with Implicit Reasoning Strategies](https://mlsanity.com/paper/2101.02235/) (2021)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [Dynamic Early Exit in Reasoning Models](https://mlsanity.com/paper/2504.15895/) (2025)
- [Know Your Limits: A Survey of Abstention in Large Language Models](https://mlsanity.com/paper/2407.18418/) (2024)
- [Soft Thinking: Unlocking the Reasoning Potential of LLMs in Continuous Concept Space](https://mlsanity.com/paper/2505.15778/) (2025)
- [Learning to Route LLMs with Confidence Tokens](https://mlsanity.com/paper/2410.13284/) (2024)
- [Effectively Controlling Reasoning Models through Thinking Intervention](https://mlsanity.com/paper/2503.24370/) (2025)
- [Do LLMs Know When to NOT Answer? Investigating Abstention Abilities of Large Language Models](https://mlsanity.com/paper/2407.16221/) (2024)
- [Language Models Are Capable of Metacognitive Monitoring and Control of Their Internal Activations](https://mlsanity.com/paper/2505.13763/) (2025)
- [There Will Be a Scientific Theory of Deep Learning](https://mlsanity.com/paper/2604.21691/) (2026)
- [Privileged Self-Access Matters for Introspection in AI](https://mlsanity.com/paper/2508.14802/) (2025)
- [Can LLMs Predict Their Own Failures? Self-Awareness via Internal Circuits](https://mlsanity.com/paper/2512.20578/) (2025)
- [To Call or Not to Call: A Framework to Assess and Optimize LLM Tool Calling](https://mlsanity.com/paper/2605.00737/) (2026)
- [LLMs Should Express Uncertainty Explicitly](https://mlsanity.com/paper/2604.05306/) (2026)
- [Who Flips? Self- and Cross-Model Counterarguments Reveal Answer Instability in LLMs](https://mlsanity.com/paper/2606.16011/) (2026)

## Abstract (arXiv)

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.