With rising interest in the topic of judges as mediators, I am recirculatating the article published last year on this topic. The article reviews prominent accountability measures for judges and how these systems may not operate effectively when judges serve as mediators, especially when lawyers and parties have strong disincentives to object as needed. Given the objective of maintaining the legitimacy of the court system to the public, the appearance of impropriety is a major basis of concern throughout judicial ethics, whether or not there is evidence of actual inpropriety. Again, here is the article.