Bettors simply aggregated the opinions of the pundits, the statisticians and media, and their sheer number averaged it out. Without access to the media, the bettors would not have enough information to be as accurate.
What the markets are are just an averaging of more informed opinions - look what happened when Sarah Palin got picked - the media hyped that up, and the bettors went with it.
The opinion of bettors is not a simple aggregate though. They weight information based on what they believe to be most credible. A mildly credible source isn't worth putting at risk.
There's a selection bias in the people who bet on elections. You only bet if you think you know something other people don't -- if you're wrong you lose your money. If you're wrong as a pundit, nothing happens. As they say, the bettors put their money where their mouth is.
There's an interesting counterargument: people who use prediction markets to hedge against the outcome they don't want. I don't know how many people actually do this, though.
What the markets are are just an averaging of more informed opinions - look what happened when Sarah Palin got picked - the media hyped that up, and the bettors went with it.