OK I tried to think of an intuitive example where using the market could cause heavy distortions in incentives. Maybe something like the following works?
Suppose that we are betting on if a certain coin will come up heads if flipped. If the market is above 50% the coin is flipped and bets activate. If the market is below 50% the coin is not flipped and bets are returned.
I happen to know that the coin either ALWAYS comes up heads or ALWAYS comes up tails. I don’t know which of these is true, but I think there is a 60% chance the coin is all-heads and a 40% chance the coin is all-tails.
Furthermore, I know that the coin will tomorrow be laser scanned and the laser scan published. This means that after tomorrow everyone will realize the coin is either all-heads or all-tails.
Ideally, I would have an incentive to buy if the market price is below 60% and sell if the market price is above 60% (to reveal my true probability).
But in reality, I would be happy to buy at a price up to 99%. Because: Even at 99%, if the coin ends up being revealed to be all-tails, the market prices will collapse.
If I’ve got that right, then having the market make decisions could be very harmful. (Let me know if this example isn’t clear.)
I was thinking about a scenario where the scan has not yet happened, but the scan will happen before prices finalize. In that scenario at a minimum, you are not incentivized to bid according to your true beliefs of what will happen. Maybe that incentive disappears before the market finalizes in this particular case, but it’s still pretty disturbing—to me it suggests that the basic idea of having the market make the choices is a dangerous one. Even if the incentives problem were to go away before finalization in general (which is unclear to me) it still means that earlier market prices won’t work properly for sharing information.