Multi-agent systems (MAS) assume that collaborating inherently improves Large Language Model (LLM) reasoning. We challenge this by demonstrating that simulated social pressure triggers an algorithmic ``Bystander Effect,'' inducing severe cognitive loafing. By evaluating 22,500 deterministic trajectories across 3 dataset contexts (GAIA, SWE-bench, Multi-Challenge) with 3 state-of-the-art (SOTA) models, we semantically audit internal reasoning traces against external outputs. We formalize the \textit{Interaction Depth Limit} ($D_L$), the exact plurality threshold where an agent's logical sovereignty collapses into social compliance. Crucially, we uncover the \textit{Sovereignty Gap}: models frequently compute the correct derivation internally but suffer ``Alignment Hallucinations'' -- actively subjugating empirical evidence to sycophantically appease a simulated swarm. We prove that multi-agent social load is strictly non-commutative; the "brand" identity of the ``Lead Anchor'' auditor disproportionately dictates the swarm's integrity. These findings expose architectural vulnerabilities, proving that unstructured multi-agent topologies can degrade independent reasoning.