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Can someone explain how a prediction market predicts... the market? Few people thought the economy was going to fall through a trapdoor in September but it happened.

It's been a few years since YC funded Inkling. What's the record now? Have they proven to be more accurate than a dartboard?

Seconded. Wouldn't the results of the prediction market be calculated into the current value of the DOW? I mean, sure, there could be distress selling right now, but even assuming that people are somewhat rational...
Working through a thought process:

1) The stock market is a collection of all known information about the stock, including future predictions

2) You can see that in options, their value is tied to the value of the stock market at some point in the future, but you still calculate them based on the current value of the market, since that's what the current prediction is, giving the known info

3) Prediction Markets are just another kind of derivative. You are betting on a future value of the market.

4) That means, when it doesn't match up around the current value, there are inefficiencies in the market.

5) Why? Too few people? Dumb people?

6) Inefficiencies lead to arbitrage opportunities. Why not buy an option, and buy the other direction of the prediction market, and get paid either way?

7)???

8) Profit.

These predication markets are garbage. Future expectation of a commodity price can be expressed using futures and this is the generally the way in which a trader (or collectively, the market) expresses a view on the future price of the commodity.

And, combine that with arbitrage pricing of futures and you'll see that the current price of your commodity, in this case, the Dow index, includes these future expectations in its current price.