One of the potential values of a prediction market for judicial decisions would be the ability for third-parties to effectively purchase legal rights to judgments. Depending on the likelihood of success, markets could be created whereby parties can get in on the action!
This article may also be of interest.
Third party litigation funders provide non-recourse loans to plaintiffs who repay these loans if and only if they prevail. This means that the interest rates funders charge reflect the funder’s information about the strength of the plaintiff’s case. We analyze a signaling model in which the plaintiff can introduce its funding contract as evidence. If the funder’s information or evaluation is informative, then funder’s have an incentive to signal that the plaintiff has a strong case to increase their chance of recovery. We show that there exists a separating equilibrium in which the funder’s information is fully-revealed. Furthermore, under some conditions, the need to signal forces the funder to charge plaintiffs a lower interest rate and increases the probability of efficient loans taking place.
A prediction-market would be quite useful for such a project to signal interest in case, and permit hedging of bets on good cases. I would cite from the article but it says do not cite, so I won’t.