The Minnesota Code of Judicial Conduct at Rule 3.9 allows retired and part-time judges to serve as private neutrals in limited circumstances. Judges may not act as a mediator or arbitrator during judicial assignments. They also may not serve as a neutral on a case where they previously acted as a judge without the parties' consent.
Minnesota Code of Judicial Conduct Rule 3.9: Service as Arbitrator or Mediator
Minnesota Supreme Court. Dec. 18, 2008https://www.revisor.mn.gov/court_rules/rule/prjudi-toh/