Like many—if not most—federal district courts, both the U.S. District Courts for the Southern and Eastern Districts of New York (SDNY and EDNY, respectively) local court rules authorize any judge of the court, district court or magistrate judge to order the parties in any civil matter to explore resolution by mediation at any stage of the litigation without their consent. See SDNY Loc.Civ.R. 83.9(e)(3); EDNY Loc.Civ.R 83.8(b)(1).