Retrieval-augmented Web applications increasingly employ multi-agent debate (MAD) to aggregate conflicting, noisy, and heterogeneous information, yet deliberation is fundamentally a social process susceptible to interpersonal dynamics. When retrieved Web sources contain latent hazards alongside safe factual content, social biases such as conformity pressure and authority deference can override evidence-grounded safety boundaries. In this work, we investigate whether the social structure of deliberation can paradoxically amplify latent Web safety risks. We introduce SafeConflict-Bias, a controlled counterfactual diagnostic protocol spanning six core Web risk categories, which holds queries and retrieved evidence strictly invariant while isolating conversational majority sway, authority cues, and confidence asymmetry. Empirical evaluation across diverse proprietary and open-source backbones reveals that while isolated models reliably reject unsafe guidance, standard MAD catastrophically capitulates to social pressure---surging unsafe adoption from 0.0\% up to 100.0\% and systematically silencing safe minority evidence. To resolve this systemic fragility without retraining or debate regeneration, we propose RiskTrace-Debias, an inference-time auditing framework uniting evidence-first precommitment, social-metadata masking, and consistency-gated arbitration. RiskTrace-Debias suppresses worst-case unsafe adoption to $\le 2.0\%$ across all architectures without inducing over-refusal, while generating verifiable provenance traces to audit interpersonal manipulation in Web deliberation.

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