The Accountability Horizon: an impossibility theorem for AI governance
A new impossibility theorem says that once agents get autonomous enough, no framework can pin responsibility on a single person.
A paper from Haileleol Tibebu and Hewan Shemtaga proves what the authors call the first impossibility result in AI governance.
Most accountability frameworks rest on one assumption: when something goes wrong, at least one identifiable person had enough involvement and foresight to answer for it. The authors formalize joint human-AI systems as Human-Agent Collectives and name four minimal properties a legitimate accountability regime should hold. Responsibility should track causal contribution. It should not exceed what an agent could foresee. At least one agent should carry real responsibility. And all of it should be allocated. The theorem: once a collective's autonomy passes a threshold they call the Accountability Horizon, and its agents form a feedback loop with humans, no framework can hold all four at once. Transparency, audits, and oversight do not fix it without reducing autonomy.
Below that threshold, the frameworks legal teams build today still hold. Above it, responsibility stops being something you can pin to one actor, and accountability has to live in the system's own record of what the collective did and why. Most enterprise governance is still designed to supervise agents one at a time. That is the assumption this paper says breaks.