In fact there was a big push in 2010 to build a betting market type system for analysis across the Intelligence Community. It is not used 100% of the time but has some measure of success where applied.
When I was in the IC I actually built a hypothesis estimation tool based on the Delphi method and a Bayesian updater to give probabilities for future events, crowdsourcing the votes from the community. Worked ok in our limited run, but needed a lot more work to implement really well.
But I was approaching it very differently than I would if it was my job. Since the system that was set up gave high rewards to unpopular predictions, I just gambled on the few most unpopular that had at least some shot at reversing. It wasn't the smartest approach, but it was the most fun. If I was doing it for real, obviously I'd go a different way.
The people who did best, at least from what I saw, tended to ride waves of popularity on the more active questions, buying low and selling high.
What I did was like betting on a few biotech startups, what the best scorers did was like riding waves of the market leading stocks.
In the end, I'm not that sure it had much to do with actual prediction of events. Then again, neither did my approach. I guess I'm not sold on the version of prediction markets they were using.
Our company (Cultivate Labs) recently acquired Inkling Markets (a very early YC company that built prediction market software) and have been building a new version of the PM platform, which will hopefully address some of the risk/reward quirks.
If you're interested in this stuff, you might be interested in the two topical PM sites we're launching: -https://sportscast.cultivateforecasts.com/ (obviously focused on sports) -https://alphacast.cultivateforecasts.com/ (officially launching later this week, focused on global finance, politics, & tech).
I'll definitely check out your new sites.