Epistemic Filtering and Collective Hallucination: A Jury Theorem for Confidence-Calibrated Agents

We investigate the collective accuracy of heterogeneous agents who learn to estimate their own reliability over time and selectively abstain from voting. While classical epistemic voting results, such as the \textit{Condorcet Jury Theorem} (CJT), assume fixed participation, real-world aggregation often benefits from allowing agents to say ``I don't know.'' We propose a probabilistic framework where agents engage in a \textit{calibration} phase, updating beliefs about their own fixed competence, before facing a final confidence gate that determines whether to vote or abstain. We derive a non-asymptotic lower bound on the group's success probability and prove that this \textit{selective participation} generalizes the asymptotic guarantees of the CJT to a sequential, confidence-gated setting. Empirically, we validate these bounds via Monte Carlo simulations. While our results are general, we discuss their potential application to AI safety, outlining how this framework can mitigate \textit{hallucinations} in collective LLM decision-making.