It is generally something that is agreed to by both sides. Either party can request a mediation. Obviously, both parties need to be in agreement for the Mediation to be meaningful.
Sometimes the court requires mediation. Sometimes the parties agree to do it. For a mediation to succeed, both sides have to want to settle. A mediation is as much a test of lawyers' skill as any other part of a case. Never go into a mediation without a good, well prepared lawyer on your side..
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Mediation has become very common but not required. Either side can suggest it but both side must be willing to settle the claim for mediation to be an option.
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If the case is in Federal Court the Court will mandate the parties engage in mediation. In state court both sides have to agree. Generally since the defendant has the money they need to be the one to suggest mediation.