What if the twelve jurors of Sidney Lumet's 12 Angry Men (1957) were not men, but large language models? Would the one juror who disagrees still be able to change everyone's mind? This paper instantiates that scenario as a multi-agent benchmark for LLM deliberation: twelve agents, each conditioned on a film-faithful persona, debate the film's murder case using multi-agent framework. Two models representing opposite ends of the RLHF spectrum are tested: GPT-4o (closed-source, heavy alignment) and Llama-4-Scout (open-weight, lighter alignment), across three conditions (baseline, open-minded prompt, no initial vote), with N = 3 replications per cell (18 runs total). Three findings emerge. (i) Seventeen of eighteen runs end in a hung jury (a state where the jury fails to reach a unanimous verdict); the film's central event, gradual minority-to-majority persuasion, almost never occurs, indicating that anchoring is the dominant failure mode of current LLMs in this setting. (ii) The two models exhibit sharply different internal dynamics: GPT-4o produces a mean of 1.0 vote changes per run across all conditions, while Llama-4-Scout ranges from 2.0 (baseline) to 6.0 (open-minded prompt), and is the only model to reach a NOT\_GUILTY verdict (1 of 3 runs in the no-initial-vote condition). The same ``open-minded'' instruction is internalized by Llama and ignored by GPT-4o. (iii) This asymmetry suggests that the intensity of RLHF alignment training, not model capability, is the primary determinant of deliberative flexibility in multi-agent settings. Flexibility, not capability, tracks human deliberation. The work is framed as an exploratory study and discusses implications for jury-of-LLMs evaluation and multi-agent debate.