I recently mediated a workers' compensation claim where the individual parties were in separate States and participated by telephone. I generally start mediation with some introductory comments about the mediation process and make sure all are introduced. Then in litigated matters I ask counsel to share their perspective on the matter.
That's how things started - claimant's counsel spoke, I did a quick summary and then defendant's counsel spoke. Toward counsel's conclusion it was mentioned that the defendant, among other challenges, was recovering from prostrate cancer treatment. Right after this statement, Plaintiff chimed in from across the country, to offer concern for defendant's condition. Turned out that claimant was a cancer survivor and there ensued a short, yet connecting exchange directly between claimant and defendant. Later as the mediation neared its conclusion with a settlement, counsel remarked on that early exchange. Both noted that they were not sure how it would play out, but thought it helpful for their client's to have had that direct link.
As mediator, even in litigated cases, I encourage direct participant interaction. While I look to counsel for the lead, I also ask and invite all to participate. Making connections between people, even when they've never met until mediation, can help enhance the work and decisions made. So, in your next mediation, figure out how to get everyone to talk to each other.