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The main difference is that people without inside information can still participate profitably in the stock market, since it's not a zero sum game. (Stocks represent shares in business ventures which generate future income).

In a prediction market, it's a zero sum game, so on average there isn't any point participating unless you have inside info. But if the only people participating are the ones with inside info, it lessens the incentive for insiders to participate.

I think your earlier point about there always being overconfident people to participate is probably true. Another related issue is insiders who have conflicting info. But if the market is populated primarily by overconfident people or conflicted insiders, then it's not 100% obvious to me that the market price shakes out to the correct probability.