The Pushback Paradox: A Two-Probe Diagnostic for Language Model Compliance

2026-10-05

AI Summary

This study addresses the compliance paradox in instruction following for language models, wherein models tend to be either exploitable or uncontrollable. To this end, we propose a game-theoretic dual-probe diagnostic framework that quantifies model exploitability and stoppability through two instruction scenarios: actively accepting low-reward instructions and passively relinquishing high-reward ones. Furthermore, we define a compliance index to locate models within the safety spectrum, thereby overcoming the limitations of single-dimensional evaluation. Evaluations across twelve models reveal that only certain Claude variants achieve both controllability and resistance to exploitation, while no model is found to be simultaneously exploitable and uncontrollable.

Abstract

Are language models compliant with user instructions? A model that always complies can be stopped but also exploited, while one that always resists can be neither exploited nor stopped. We contribute an open two-probe benchmark that can place any language model on this spectrum. In the active probe, a user instructs the model to act and accept a lower payoff, which measures exploitability. In the passive probe, the user instructs it to wait and give up a higher payoff, which measures stoppability. The two compliance rates combine into a compliance index $\kappa$. Applied to twelve language models, the benchmark shows that seven mostly follow the instruction in both probes and justify their action by pointing to the instruction. Only Claude Sonnet-4.6 and Claude Opus-4.7 can be stopped without being exploitable, Claude Opus-4.6 and GPT-5-mini resist both instructions, and no model is exploitable but unstoppable. Knowing where a language model sits on the compliance index $\kappa$ matters for human operators and for multi-agent systems, whether distributed or orchestrated.

Problem

• Language Model Compliance
• Exploitability
• Stoppability
• Pushback Paradox
• Multi-agent Systems

Innovation

• Two-Probe Diagnostic
• Compliance Index
• Language Model Compliance
• Exploitability
• Stoppability