In the May/June 2006 issue of AARP Magazine I found a blurb about this new practice (unfortunately, I haven't found a link for this particular article). Writer Laura Daily reports that while most popular with celebrities (Brad Pitt and Jennifer Aniston hired a judge to handle their divorce proceedings) the benefits are attracting ordinary folk as well, due in part to the savings in time and money:
Booking your own judge means your lawyer and expert witnesses aren't sitting running the meter while a jurist hears some other case, notes Kathleen Robertson, who practices family law in Los Altos, California. The rental can cost $350 to $475 an hour (a rate you split with your opponent), but because most cases are settled in days instead of weeks, "using a private judge can save 30 to 50 percent in time and fees," she says.
Other benefits include bypassing clogged court systems, the ability to pick a judge who specializes in that type of case, and, unlike arbitration, the decision can still be appealed.
Renting a judge is a practice already in use in California, Colorado and Ohio, with Texas and Florida soon to follow.