Meet with one party...tell them how bad their position is...get them to worry about the worst case scenario.
Then, meet with the other party...tell them how bad their position is...get them to worry about the worst case scenario.
Mediators always come on hard.
Then, they work to bring the parties together.
The hard playing is not the end goal. It is the opening gambit. It also makes each party look good when compromise is reached. The lead on each side can go back and say, "Sure, we had to give up X, but we didn't have to suffer through the worst case of 10X, so I won with the compromise." It allows saving face. When the other side gives in, they can still go to their people and say they gained something.
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