I have published some research on using LLMs for mediation here: https://arxiv.org/abs/2307.16732 and https://arxiv.org/abs/2410.07053
These papers describe the LLMediator, a platform that uses LLMs to:
a) ensure a discussion maintains a positive tone by flagging and offering reformulated versions of messages that may derail the conversation
b) suggest intervention messages that the mediator can use to intervene in the discussion and guide the parties toward a positive outcome.
Overall, LLMs seem to be very good at these tasks, and even compared favourably to human-written interventions. Very excited about the potential of LLMs to lower the barrier to mediation, as it has a lot of potential to resolve disputes in a positive and collaborative manner.