Who's the judge that will decide who is lying and just being paid to lie? When he decides, who will enforce his ruling or is his judgement (if there even is a judge) just for informational purposes only, like the bitcoin police?
Private arbitration is already being used, and while the arbitrator's decision would not have the threat of force if the loser of the case did not comply, breaking that contract would make you an outlaw, not protected by the laws you denounce. As I said, if you refuse the judicial process, that leaves only the old-fashioned art of vendetta.
As I recall, you also approve of lynch mobs for situations like this.