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 be of some use:

This paper examines the law and economics of third-party financed litigation. I explore the conditions under which a system of third-party financiers and litigators can enhance social welfare, and the conditions under which it is likely to reduce social welfare. Among the applications I consider are the sale of legal rights (such as contingent tort claims) to insurers, to patent trolls, and to financiers generally.

And on markets:

I also examine a market in which contingent claims are auctioned to a financier who then assigns them to enforcers. The bids offered by the financier reflect the type of litigator (enforcer) to whom the financier will assign the claim. When the auction market is efficient, in the sense that it enhances society’s wealth, there are still inefficient transfers of legal rights that could occur. If the auction market is inefficient – e.g., because sellers set the wrong prices for their rights – the problem of inefficient transfers of legal rights is even worse.

I wonder if the author Keith N. Hylton is related to Hylton of Ware v. Hylton fame?