https://huggingface.co/papers/2306.05685
This paper makes the argument that...
"Our results reveal that strong LLM judges like GPT-4 can match both controlled and crowdsourced human preferences well, achieving over 80% agreement, the same level of agreement between humans. Hence, LLM-as-a-judge is a scalable and explainable way to approximate human preferences, which are otherwise very expensive to obtain."
So, the Arena could theoretically be automated and achieve similar outcomes. Or at least, it could quickly determine a predicted-ELO for every model, which would be interesting to compare against the human-rated outcomes.