The rapid advancement of Large Language Models (LLMs) necessitates robust and challenging benchmarks. Leaderboards like Chatbot Arena rank LLMs based on how well their responses align with human preferences. However, many tasks such as those related to emotional intelligence, creative writing, or persuasiveness, are highly subjective and often lack majoritarian human agreement. Judges may have irreconcilable disagreements about what constitutes a better response. To address the challenge of ranking LLMs on highly subjective tasks, we propose a novel benchmarking framework, the Language Model Council (LMC). The LMC operates through a democratic process to: 1) formulate a test set through equal participation, 2) administer the test among council members, and 3) evaluate responses as a collective jury. We deploy a council of 20 newest LLMs on an open-ended emotional intelligence task: responding to interpersonal dilemmas. Our results show that the LMC produces rankings that are more separable, robust, and less biased than those from any individual LLM judge, and is more consistent with a human-established leaderboard compared to other benchmarks.