Andrew: I favor Bryan Caplan's explanation: when a belief you hold starts to have material consequences for you, when before it did not, your brain switches to more "realistic" thinking. From introspection, I find this to be true. It's a great experiment you can do on yourself anytime. Think about something you believe strongly, and then consider taking an offer to put money on it. In my experience -- and I'm the only one I can observe for this -- I get a weird feeling, like a complete perception shift. (If I studied psychology, I might toss in a "Gestalt" somewhere.)
Eliezer_Yudkowsy is right: If you really believe something will happen, and you like money, and betting that it will happen will get you more money, that implies that you should make the bet. (Issues about the bookie can be resolved by having a friend secure the bet.) The refusal to bet therefore suggests the person is being dishonest about his stated level of certainty. I believe Robin_Hanson has made a good point before about how claims like "Oh, Hillary can't win, I know it" shouldn't be read as actual claims of knowledge, but a "signal" about whose "team" you are on, and therefore asking to bet misses the real point of that person in making that statement.
The Intrade prediction market is giving Hillary a 53% chance and Obama a 47% chance of winning the Democratic presidential nomination. Hillary is down 7.5 percentage points in just the last day. (Note: Between when I wrote the above, and when I posted this, Hillary went up to 54.)
From what I've read on Intrade, you can fund your account with up to $250 using a credit card, and it should land in your account immediately. (More than this takes time.) Also, remember that you can sell contracts at any time afterward - you don't have to wait months to collect your payout.
If you think that Hillary is going to do better than the polls on Super Tuesday, and you're going to sneer afterward and say that Intrade was "just tracking the polls", buy Hillary now.
If you think that Obama is going to do better than the polls on Super Tuesday, and you're going to gloat about how prediction markets didn't call this surprise in advance, buy Obama now.
If you don't do either, then clearly you do not really believe that you know anything the prediction markets don't. (Or you don't understand expected utility, or your utilities over final outcomes drop off improbably fast in the vicinity of your current wealth minus fifty bucks - you don't have to bet the full $250.) It is free money, going now for anyone who genuinely thinks they know better than the prediction markets what will happen next.
Prediction markets do not have supernatural insight. If they give the candidates fifty-fifty odds, it means that the market collectively doesn't know what will happen next. Even if you're well-calibrated, you get surprised on 90% probabilities one time out of ten.
The point is not that prediction markets are a good predictor but that they are the best predictor. If you think you can do better, why ain'cha rich? Any person, group, or method that does better can pump money out of the prediction markets.
If prediction markets react to polls, they're getting new information, that they didn't predict in advance, which happens. Being the best predictor doesn't make you omniscient.
Everyone's going to find it real easy to make a better prediction afterward, but if you think you can call it in advance, there's FREE MONEY GOING NOW.
Buy now, or forever hold your peace.