One of the ten disruptive technologies presented by Richard Susskind at ILTA 2009 was online dispute resolution. He specifically mentioned SquareTrade and CyberSettle.
In his remarks, Susskind explained the double-blind method where two parties can come to terms without disclosing their ultimate position to the other side. One side submits to the online system the maximum that they would be willing to pay to resolve a claim and the other side submits the minimum they would accept. The system tells them when they are within a predetermined range, so they know they are close to a compromise settlement.
It makes me wonder whether competitive bids for fixed fees might adopt a similar procedure. A law department could upload the maximum it would pay while the bidding firms upload the minimum they would accept. An online system would find the strike point.