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"that a prediction market effectively liberates the directional content of that information by converting it into prices."
I can see this, and I guess maybe my issue is with the phrasing of "aggregating" insider information. Because you aren't just aggregating insider info, you are also aggregating non-insider information, but no one (but the insider) knows what is right.
Is there different types of prediction markets then? One where there is a true insider and one without? For example, you could take bets on weather it will rain on Saturday. People can make educated guesses, but no one really knows (no insider). On the flip side, Kanye could create a bet on whether he will run for president. He would be the only insider, so again, aggregating insider and non insider information.