Especially as a mediator, listen to the parties' perspectives without taking sides or evaluating who is right or wrong. Before you begin discussing one issue, know what all the issues are so that they can be discussed in their order of importance start the discussion with the least important issue and work toward the harder ones. Statements require rebuttal, questions allow for reflection. The positional statements most people make are defensive responses which reflect of their fears and concerns. Addressing the underlying concern can often open-up acceptable options.
Logic is an ineffective way to convince someone.
Give parties time to assimilate shifts in their perspectives. Use parties' resistance to your advantage and don't try to confront what appears to be poor logic. Don't push people to decide on the spot. Focus on substantive conflicts. Written settlement offers or recommendations do not work writings are usually taken to be hard and fast positions that cut off or disallow discussion of other options.