Mediation should provide parties new paths toward resolution.
One approach I find very effective is explaining the differences between litigation and mediation this way: Litigation and mediation are polar opposite approaches to ending a conflict. Litigation is entirely focused on the past – what happened. Mediation is about present and future circumstances.
One you have no control over. One you do.
I regularly see parties in negotiations suddenly able to make progress when I ask them to consider how an offer strikes them when viewed with a forward focus – whether it enhances their present and future circumstances more than remaining in litigation does.
Helping them look in another direction (away from the past and associated comparisons of case strengths/weaknesses, risks/benefits, right/wrong, etc.) shows them there’s a different kind of analysis available, and sheds light on new litigation exit doors.