Yep, I just wish people could bet on these predictions too. Unfortunately, that is illegal in the US ...
More specifically, they are called prediction markets. They are legal and have been around for a while. You can even bet on the weather if you like! Enron came up with the idea of Weather Futures (aka Weather Derivatives) in their heyday, and these investment instruments are still used for hedging.
As far as I know, http://www.intrade.com/ lets you bet on elections and similar current events. Can't tell you how legitimate they are though.
Intrade is based in Ireland and is illegal for US users. The Iowa Markets got a special exemption from the FTC as an academic research project.
And you can't sell derivatives unless you get regulator approval (which they won't give for betting markets) (see http://hanson.gmu.edu/ideafutures.html, for example).
Hanson (a professor of Econ at GMU, and contributor at overcomingbias) is one of the strongest proponents of legal prediction markets. He (and many others) have been lobbying for them forever, with no luck.
What's surprising though is that there are already investment instruments for transferring risks associated with outcomes. These are essentially predictions too, but you can only go "short" on life, so to speak.
Catastrophe Bonds, the recently infamous Credit Default Swaps are all instruments that pay off based on an outcome. In other words, they aren't really linked to the price of any commodity directly.
So, what gives? What's the difference?
People bet differently when they have something real at stake - ever tried to play poker with no money behind the chips? It's a completely different (and completely boring) game. It's the reason the market instantly knew who was responsible for the Challenger crash (when it took Richard Feynman and the rest of genius scientists on the panel months to even have a plausible idea).
Sorry for the scribd link. It's the first copy I found that wasn't behind a pay wall.
The gist is that within a few hours of the Challenger crash the stock for the company responsible for the component that failed went down far more than the stocks for other companies involved in building challenger. Interestingly, the equity value the stock lost (~200 Million USD) is almost exactly the same as the estimated total loss in profit (fines, lawsuits, updates to safety standards, lost contracts, etc).
No one is saying we should use markets for safety investigations - we are saying that we should use it predicatively.