I've always called these "decision markets", and will do so here to simplify the language in this discussion. But that term is overused to the point of being confusing, and I'm curious if anyone can come up with a better one.
By "decision market", I mean a prediction market in which the traders are explicitly attempting to predict a decision made by the market's own judge.
About Prediction Markets:
A prediction market is usually described as being one in which the traders are attempting to predict the outcome of some future event. But in implementation, a prediction market always has a judge -- usually a single person, but sometimes a committee -- who uses their own interpretation of the event's outcome to set contract values at expiration. So in effect, a prediction market is really a market in which the traders are attempting to predict the judge's decision regarding the event.
An example of a prediction market is one in which the traded contracts represent the probability of one or more political candidates winning an election. In this case, the prospectus describes how the judge will decide who the winner was, and might reference the New York Times as an external authority on the election results. A well-written prospectus will always provide an "escape" clause, though, to allow the judge to close out contracts at a reasonable price in the face of unforeseen circumstances, such as a failure of the newspaper itself.
About Decision Markets:
An example of a decision market is one in which the traded contracts represent the release date of an open-source software package. In this example, the judge is the maintainer of the package, and the prospectus states that the judge will ultimately decide when to release the software, based not only on available information such as outstanding known bugs, but also on the price information provided by the market itself. This, for example, gives the market the opportunity to provide quantified signals regarding issues that might otherwise be hidden in mailing list discussions.
I don't know of any active decision markets. I'd like to start an open-source project for software which would support them, which leads me to the above question.