But wouldn't rational bettors' willingness-to-pay for a stake in a candidate be the same in both cases (buying for insurance vs. buying as a speculator)? Their WTP would be determined entirely by odds, right?
Example: Llewelyn has (in your view) a 5-1 chance of winning. Maxine, whom you despise, has 1-5. Let's say I offer to sell you a voucher that is redeemable for $5 in the event the hated Maxine wins (and is just worthless paper otherwise). How much would you be willing to pay for this voucher?
I can't speak for you personally, but wouldn't the money-maximizer pay up to $1 for it? (In five possible worlds, L wins and you lost a dollar; in one, M wins and you get five bucks; pay a cent more and expect to lose money.)
And my point is this: The fact that you hate Maxine was irrelevant all along. You (or, again, our hypothetical rational agent) should be willing to pay up to $1 no matter how you feel about Llewelyn and Maxine, assuming a given estimate of their likeliness to win.
If I have errred, please do point it out where my map is wrong.
Their WTP would be determined entirely by odds, right?
No. In short: with insurance you're paying money to reduce risk. Thus, WTP goes up.
How much would you be willing to pay for this voucher?
It depends how much I stand to lose regardless of betting, if Maxine wins.
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.