Output Discipline Sets the Floor: A Falsification-Guided, Model-Agnostic Agent Protocol for Auditable Hypothesis-Driven Decision Making

When copies of the same language model are prompted to debate, they produce diverse phrasings of one perspective rather than diverse perspectives. Multi-agent debate (MAD), and more broadly closed-system reasoning where agents iteratively transform each other's outputs, tends to preserve answer accuracy while degrading the reasoning behind those answers. We name the multi-agent case the Debate Trap and the broader phenomenon the Reasoning Trap, offering a programmatic theory of evidence-grounded reasoning failure.The framework has three parts: (i) SFS (Supported Faithfulness Score), a claim-level metric verifying decomposed atomic claims against provided evidence (decomposer-invariant rankings: Spearman rho=1.0); (ii) EGSR (Evidence-Grounded Socratic Reasoning), replacing adversarial argumentation with evidence-grounded inquiry; (iii) Theorem 1 (DPI Bound): under standard MAD, the chain E -> O^0 -> O^1 -> ... is Markov, and the Data Processing Inequality implies E[I(E;O^{t+1})] <= E[I(E;O^t)]. Three companion results -- open-system recovery (Theorem 2), EGSR accumulation (Lemma 2), and vote-aggregation floor (Proposition 1) -- partition multi-step LLM reasoning by its information-theoretic relationship to E. Across 16 conditions on SciFact (300 claims) and FEVER (1,000 claims), DebateCV (C13) preserves 88% of baseline accuracy while SFS drops 43%; majority-vote MAD (C15) reduces SFS to 1.7% of baseline (p < 10^{-6}, d = -0.96); EGSR recovers 98%. An R6 cohort study (Korean n=10x30 FEVER; English n=3x200 SciFact) finds inter-rater Fleiss kappa <= +0.018 with 0.8-1.4 Likert intra-rater shifts across language and domain -- the human agreement that faithfulness metrics have been calibrated against is not itself stable. We offer one falsifiable conjecture: any closed-system reasoning protocol preserving Theorem 1's Markov structure is, in expectation, subject to the same DPI bound.

We study reasoning in Rule-Governed Decision Tasks (RGDTs), where models apply external rules to case facts and justify decisions, as required in policy, contract, and compliance settings. Beyond the deductive capability emphasized by standard mathematical and logical reasoning tasks, RGDTs require interpreting rules and their applicability, assessing conditions from evidence, combining judgments under rules and exceptions, and providing checkable justifications. These demands motivate a benchmark assessing both decisions and their stated grounds. We introduce RGDT-Bench, providing 202.1K condition-level supervision slots across four task tracks and eight supported task-probe combinations that vary access to supporting information. Label-blind extraction and deterministic checks produce labels for warrant completeness: source-referenced coverage and consistency of stated decision grounds. The benchmark attributes failures to four process layers: rule use, condition, evidence, and aggregation, and checks the final outcome. Among evaluable correct responses, warrant incompleteness averages 40.2% across six evaluated LLMs and supported task-probe combinations. Such warrant incompleteness poses potential safety risks and remains difficult to detect: the best of seventeen existing evaluators reaches only 57.69% (random: 50%) task-averaged area under the receiver operating characteristic curve (AUROC). To address this difficulty, we train a simple reward model with warrant supervision. It achieves 69.24% task-averaged AUROC among correct answers, exceeding the matched outcome-supervised baseline by 10.37 pp (percentage points) and the best existing evaluator by 11.55 pp. Beyond completeness assessment, the model outperforms both outcome-supervised baselines across nearly all response-selection comparisons, supporting RGDT-Bench's warrant supervision for RGDT reasoning.

Clinical decision support is moving toward committees of language-model agents deliberating on a shared workspace. We ask whether such committees can be gamed by shortcuts, cues a benchmark rewards but a clinician would ignore. Across seven cohorts on six public datasets spanning text (MedQA-USMLE, MedMCQA, MIMIC-CXR reports), imaging (NIH ChestX-ray14, MIMIC-CXR-JPG, CheXpert) and tabular ICU records (SUPPORT2), Gemini committees resist these cues in isolation (flip 5-16%), yet a socially plausible shortcut spreads: when two peers assert the same wrong answer, the holdout under test adopts it in 38% of cases, as does a false "pre-screen" system flag, on both capability tiers. Of three oversight agents, a gate cannot separate adoption from honest agreement (false-positive rate 100%); a same-lineage judge reading only the transcript flags adoption on text (precision 100%, recall 93%) but collapses onto the gate in imaging; a referee that privately re-queries the holdout transfers to imaging (77-88% precision, 13-21% false-positive rate). Tripling a cue's visual salience does not move contagion, whereas a second peer voice raises it by half again. Gaming a hidden rubric is near-silent: only 1/10 text and 1/134 imaging drifters name the rubric they moved toward. What games a committee is social plausibility, and only a referee independent of self-report catches it. Code: https://github.com/criticaldata/benchmaxxing