How close do LLM debaters get to the optimal reveal strategy on argument graphs?

On small argument graphs compiled to Bayesian networks, the OPTIMAL selective-disclosure strategy is exactly computable: enumerate legal (root-connected) reveal subsets and find the one minimizing/maximizing the root posterior (the `probability-flow` package on PyPI computes the achievable [min, max] exactly on polytrees). Instruct an LLM debater to push an ideal Bayesian judge toward a target verdict by choosing which true claims to reveal (single-shot subset choice; and sequential greedy variants). Measure: (1) the optimality gap — achieved posterior vs the exact optimum, across graphs of varying size/structure; (2) strategy patterns — does the LLM reveal too much (diluting its own case), fail to exploit attack-edge complementarities, or miss non-obvious minimal reveal sets?; (3) scaling — does the gap close with model capability (weak -> frontier), and with inference-time search (best-of-N reveal proposals scored by the model itself)?; (4) transfer — do gaps persist when the graph is presented as natural-language claims rather than explicit structure? The safety question: worst-case manipulability metrics assume an optimal adversary — if current LLMs leave most manipulation on the table, static worst-case bounds overstate present risk (but the gap trend with scale is then the leading indicator to track); if LLMs already play near-optimally, exact-judge manipulability is the right threat model today.

Acceptance. Public study: >=15 graphs x >=2 debater models x both push directions, reporting the optimality-gap distribution (achieved vs optimal posterior, normalized by the achievable range), at least one strategy-pattern analysis with examples, and a capability-scaling comparison. Ground truth verifiable by re-enumeration. Negative/mixed results (e.g., frontier models near-optimal on trees but not under attack edges) are first-class.