When one-at-a-time AI evaluation does not compose

Personal AI systems are usually evaluated one at a time. Their users, however, do not live independently of one another. Consider two people who influence each other’s behaviour. Each uses a personal AI that observes and advises only its own user. The systems do not communicate, share information or coordinate their actions. Yet an intervention by one AI can change the circumstances encountered by the other. The connection runs through the people. This paper examines a consequence of that connection: two AI systems can each improve the measured dynamics of a shared human system when introduced separately, while their simultaneous deployment makes that system unstable. Using a deliberately simplified dynamical model, we derive exact conditions under which this occurs. We then examine whether the result survives changes in the model’s assumptions. The analysis extends from a symmetric two-person system to asymmetric relationships and larger networks, including differences in deployment density, network structure, directionality, policy parameters and short delays. The underlying mathematics belongs to established control and network theory. The contribution is to show why it matters for personal AI evaluation. Evidence that an AI performs well when deployed alone does not necessarily establish how it will perform when other independently operated systems are influencing the same human relationships. These are mathematical and computational results, not observations of real-world AI deployments. They establish a possible failure of one-at-a-time evaluation, not its prevalence or consequences for human welfare. The accompanying reproducibility package provides the code, synthetic data and documentation used to generate the numerical results.