Well, I can imagine a post on SSC with 5 statements about the next week, where other users would reply with probabilities of each becoming true, and arguments for that. Then, after the week, you could count the scores and name the winners in the OP. It would probably get a positive reaction. Why not give it a try?
I'm not sure what the 5 statements should be though. I think it must be "next week" not "next year", because you can't enjoy a game if you've forgotten you're playing it. Also, for it to be a game, it has to be repeatable, but if you start predicting the most important events of the year, you'll run out very fast. On the other hand, weekly events tend to be unimportant random fluctuations. I think that's a big problem with the whole idea.
One possible solution could be to do experiments rather than predict natural events, i.e. "On day X I will try to do Y. Will it work?".
So, I've been thinking about prediction markets and why they aren't really catching on as much as I think they should.
My suspicion is that (beside Robin Hanson's signaling explanation, and the amount of work it takes to get to the large numbers of predictors where the quality of results becomes interesting) the basic problem of prediction markets is that they look and feel like gambling. Or at best like the stock market, which for the vast majority of people is no less distasteful.
Only a small minority of people are neither disgusted by nor terrified of gambling. Prediction markets right now are restricted to this small minority.
Poker used to have the same problem.
But over the last few decades Poker players have established that Poker is (also) a sport. They kept repeating that winning isn't purely a matter of luck, they acquired the various trappings of tournaments and leagues, they developed a culture of admiration for the most skillful players that pays in prestige rather than only money and makes it customary for everyone involved to show their names and faces. For Poker, this has worked really well. There are much more Poker players, more really smart people are deciding to get into Poker and I assume the art of game probably improved as well.
So we should consider re-framing prediction the same way.
The calibration game already does this to a degree, but sport needs competition, so results need to be comparable, so everyone needs to make predictions on the same events. You'd need something like standard cards of events that players place their predictions on.
Here's a fantasy of what it could look like.