Whether AI assistance helps or harms a population depends less on the model's accuracy than on whether people rely on it appropriately trusting it when it is right and checking it when it is not. Yet reliance is usually studied one user at a time. We model it as a population process: agents repeatedly solve a task alone, accept an AI answer, or verify it, updating a Bayesian belief about AI quality and, when networked, learning from peers. Four results form one story. The environment sets the baseline: task difficulty and AI quality fix both overreliance and calibration regret. Social learning creates consensus, not overreliance: a mean-preservation theorem, confirmed by a 2*2 topology*tagging design, shows connectivity moves the aggregate only when influence transmits beliefs. Social proof turns reliance into a feedback cascade: visible unverified use suppresses verification and tips the population into collective overreliance. Feedback design can prevent collapse: making verification visible or dampening social proof reverses it. Together, the results frame AI reliance as a computational social dynamics problem, where individual learning, peer observation, and feedback exposure jointly shape whether a population remains calibrated.

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