Implement an "LLM Council" in multiple-LLM chat

Based on karpathy’s idea : https://github.com/karpathy/llm-council

The idea is that instead of asking a question to your favorite LLM provider (e.g. OpenAI GPT 5.1, Google Gemini 3.0 Pro, Anthropic Claude Sonnet 4.5, xAI Grok 4, eg.c), you can group them into your "LLM Council". A query is sent to multiple LLMs, it then asks them to review and rank each other's work, and finally a Chairman LLM produces the final response.

In a bit more detail, here is what would happen when you submit a query:

1. Stage 1: First opinions. The user query is given to all LLMs individually, and the responses are collected. The individual responses are shown in a "tab view", so that the user can inspect them all one by one.

2. Stage 2: Review. Each individual LLM is given the responses of the other LLMs. Under the hood, the LLM identities are anonymized so that the LLM can't play favorites when judging their outputs. The LLM is asked to rank them in accuracy and insight.

3. Stage 3: Final response. The designated Chairman of the LLM Council takes all of the model's responses and compiles them into a single final answer that is presented to the user.