Designing for Accountable Agents: a Viewpoint

Existing accountability frameworks for AI systems, legal, ethical, and regulatory, rest on a shared assumption: for any consequential outcome, at least one identifiable person had enough involvement and foresight to bear meaningful responsibility. This paper proves that agentic AI systems violate this assumption not as an engineering limitation but as a mathematical necessity once autonomy exceeds a computable threshold. We introduce Human-Agent Collectives, a formalisation of joint human-AI systems where agents are modelled as state-policy tuples within a shared structural causal model. Autonomy is characterised through a four-dimensional information-theoretic profile (epistemic, executive, evaluative, social); collective behaviour through interaction graphs and joint action spaces. We axiomatise legitimate accountability through four minimal properties: Attributability (responsibility requires causal contribution), Foreseeability Bound (responsibility cannot exceed predictive capacity), Non-Vacuity (at least one agent bears non-trivial responsibility), and Completeness (all responsibility must be fully allocated). Our central result, the Accountability Incompleteness Theorem, proves that for any collective whose compound autonomy exceeds the Accountability Horizon and whose interaction graph contains a human-AI feedback cycle, no framework can satisfy all four properties simultaneously. The impossibility is structural: transparency, audits, and oversight cannot resolve it without reducing autonomy. Below the threshold, legitimate frameworks exist, establishing a sharp phase transition. Experiments on 3,000 synthetic collectives confirm all predictions with zero violations. This is the first impossibility result in AI governance, establishing a formal boundary below which current paradigms remain valid and above which distributed accountability mechanisms become necessary.

Multi-agent systems (MAS) are increasingly used in healthcare to support complex decision-making through collaboration among specialized agents. Because these systems act as collective decision-makers, they raise challenges for trust, accountability, and human oversight. Existing approaches to trustworthy AI largely rely on explainability, but explainability alone is insufficient in multi-agent settings, as it does not enable care partners to challenge or correct system outputs. To address this limitation, Contestable AI (CAI) characterizes systems that support effective human challenge throughout the decision-making lifecycle by providing transparency, structured opportunities for intervention, and mechanisms for review, correction, or override. This position paper argues that contestability is a necessary design requirement for trustworthy multi-agent algorithmic care systems. We identify key limitations in current MAS and Explainable AI (XAI) research and present a human-in-the-loop framework that integrates structured argumentation and role-based contestation to preserve human agency, clinical responsibility, and trust in high-stakes care contexts.

The increasing deployment of autonomous, agentic AI systems challenges traditional accountability mechanisms. Existing research predominantly frames AI accountability gaps as barriers that can be overcome through better standards, transparency, and institutional reform. We argue that this framing is insufficient: certain configurations of actors, systems, and institutions render AI accountability conceptually unachievable regardless of effort. We introduce the concept of constitutive AI unaccountability to capture these configurations. Through a three-stage qualitative study comprising a concept-centric literature analysis, a secondary analysis of 27 expert interviews with AI professionals from technical, legal, and sociotechnical backgrounds, and an illustrative framework application to the open-source agentic AI system OpenClaw, we identify nine categories and 20 themes of constitutive AI unaccountability. These are organized across structural, technological, and normative clusters and reinforce one another through eight directed interdependencies. Our framework is operationalized as a diagnostic instrument of 20 questions, which detected 17 of 20 conditions when applied to OpenClaw, including an inverted anthropomorphism configuration in which the AI agent was the only identifiable actor. We contribute a reframing of AI unaccountability as a constitutive property of sociotechnical systems, an extension of the four barriers to accountability, and a practical instrument for identifying accountability voids in specific AI deployments.