Incorporating Bayesian-consistent decision thresholds for tool calling in POIROT-based interrogation frameworks enables early detection of multi-agent hallucination propagation before error cascades become irreversible.

In a multi-agent LLM system using a POIROT-style interrogation/verification framework (agents cross-question each other's claims before acting on them), replacing fixed-confidence or heuristic tool-calling gates with a Bayesian-consistent decision threshold — i.e., a threshold derived from an explicit prior over hallucination rate and a likelihood ratio updated per agent turn, such that the posterior P(claim is hallucinated | evidence so far) triggers abstention/escalation whenever it exceeds a calibrated cutoff τ* — will detect the first hallucinated claim in an agent chain at least 30% earlier (measured in mean number of downstream agent turns before detection) than a fixed-threshold or no-threshold baseline, and will reduce the proportion of task runs that reach an irreversible error state (defined as: incorrect final output committed, or >2 downstream agents having incorporated the false claim into their own outputs) by at least 25% (absolute), at matched task-completion rate (within 5 percentage points of baseline) and matched computational overhead (<15% additional tool calls).

Minimum viable test (MVT): 4-agent sequential pipeline (Researcher → Critic → Synthesizer → Verifier) performing multi-hop QA and simple code-generation tasks with injected ground-truth-checkable claims. Compare three conditions: (A) no threshold (always proceed), (B) fixed-confidence threshold (static cutoff on self-reported confidence or logprob), (C) Bayesian-consistent threshold (posterior updated via likelihood ratios from POIROT cross-examination signals: contradiction rate, tool-verification mismatch, retrieval disagreement). Inject synthetic hallucinations at controlled rates (10%, 25%, 40%) into one agent's output stream via adversarial prompt perturbation or corrupted tool outputs. Measure: turns-to-detection, cascade rate, task success rate, compute overhead. N=500 runs per condition per task family, 4 task families (HotpotQA-style multi-hop, HumanEval-style code gen, tabular data QA, scientific literature synthesis) = 6,000 total runs.

# Bayesian threshold gate wrapping each agent's tool-call decision
class BayesianGate:
    def __init__(self, prior_hallucination_rate, likelihood_model, tau_star):
        self.log_prior_odds = log(prior_hallucination_rate / (1 - prior_hallucination_rate))
        self.likelihood_model = likelihood_model  # trained on POIROT interrogation features
        self.tau_star = tau_star  # calibrated decision threshold on posterior

    def update_and_decide(self, interrogation_evidence):
        # interrogation_evidence: dict of contradiction_rate, tool_mismatch,
        #   retrieval_disagreement, entropy, cross_agent_disagreement
        llr = self.likelihood_model.log_likelihood_ratio(interrogation_evidence)
        log_posterior_odds = self.log_prior_odds + llr
        posterior = sigmoid(log_posterior_odds)
        if posterior >= self.tau_star:
            return "ABSTAIN_ESCALATE"   # halt propagation, flag for review/retry
        return "PROCEED"

# Pipeline loop
for turn, agent in enumerate(pipeline):
    output = agent.act(context)
    evidence = poirot_interrogate(output, cross_agents=pipeline.others(agent))
    decision = gate.update_and_decide(evidence)
    log(turn, decision, evidence, ground_truth_check(output))
    if decision == "ABSTAIN_ESCALATE":
        output = retry_or_human_review(agent, context)
    context = append(context, output)

# Metrics harness computes: detection_turn_lag, cascade_occurred,
# task_success, tool_call_overhead per run, aggregated across conditions.