An Information-Theoretic Bound for Budget-Constrained Elicitation in Adaptive Conversational Expert Systems

Requirements analysts, clinicians, and child development specialists face the same structural problem: to elicit as much trustworthy information as possible from a human interlocutor under a hard budget of questions. Answers in such interviews are verbose and touch on several facts at once—and not always the ones asked about; self-report cannot be fully trusted; and nobody knows a principled stopping point. We formalize this class of problems as budget-constrained elicitation from a human source. The hidden state is represented by a Bayesian network over a domain graph—and it is the topology that turns out to determine the ceiling—while the state is probed through a generative observation model, a fact-cloud model that captures multi-fact answers, together with a self-report channel of bounded fidelity. The main result is a two-phase upper bound on the information attainable by any elicitation policy, including policies that mix questions with costlier verification: a linear channel phase followed by a topological plateau, with an explicit knee N* between the regimes. The bound yields a principled stopping criterion and an absolute benchmark for elicitation tools: how close a policy has come to the theoretical optimum. In addition, we prove a separation result: there exist domains where adaptive elicitation strictly outperforms any static plan with a guaranteed gap. We further show that computerized adaptive testing, static questionnaires, and slot-filling dialogue are degenerate limit points of the model's parameter space. The exposition is illustrated with examples from requirements elicitation, clinical history-taking, and child developmental assessment. This is the author's preprint of a manuscript under review at International Journal of Approximate Reasoning (Elsevier), submitted 7 September 2026, manuscript number IJA-D-26-00939. The full text is available on request from the corresponding author. Supplementary material with full proofs is included.