- From Order Books to Belief Distributions.

Markets are impressive mechanisms for information aggregation but they’re not magic. The information has to come from somewhere, and markets are inherently always living in the phase transition between stability and instability. (It is the stability that makes prices informative and the instability that allows the market to be liquid.)

I don’t see a huge problem with what Nate did either (especially since he added the caveat that he disagreed with some of the imputed beliefs). My point was just that there a lot more interesting information in the order book beyond the price at last trade. This can be used to derive a belief distribution and not just a point estimate. Regarding the interpretation of the current price, I should have said that this tells us nothing about the beliefs of traders who are not party to this transaction beyond the information in the order book. The broader point was that one needs to allow for heterogeneous priors (not just heterogeneous information) and make some assumptions about risk-preferences in order to interpret the data. Manski does indeed make some of these points, thanks for the link. But most modeling in economics is still based on the common prior assumption and confronting this was also part of the point of the post.

If you have varying account sizes, you know right away the price isn’t an evenly weighted average of beliefs, but I don’t see a huge problem with what Nate Silver wrote given his purposes. He just said they were proportional. Is someone claiming that market prices are *inversely* proportional to traders’ perceptions? Otherwise, this specific point borders on pedantry even if the broader point that market structure frustrates any interpretations of price is correct. Also I don’t really agree with the statement that the current price “tells us nothing about the beliefs of traders who are not party to this transaction.” Presumably if the other traders thought the last price was horribly off, they would move it. I agree that you can’t infer much about beliefs from the orders that are away from the market because often that is just posturing.

Some of this was addressed in what was probably the first skeptical PM paper per se, and subsequent discussion:
http://www.aeaweb.org/annual_mtg_papers/2006/0106_1015_0703.pdf

15/8 Yemen

9/4 Jordan

7/2 Algeria

7/2 Morocco

8/1 Bahrain

12/1 Iran

16/1 Libya

16/1 Sudan

16/1 Iraq

20/1 Saudi Arabia

20/1 Syria

He was talking about the InTrade market on Health Care Reform. In theory, the market price in such a derivative market should equal the expectation of the underlying event coming true. However, Paul Krugman (and many others) forgot one of the most basic assumptions of the market model! Transaction costs.

When the market price is over 95, InTrade charges a transaction fee of 3 cents per contract (real money). While market prices are quoted in percentages, the payoff for a winning ticket is $10 (real money). Therefore, the transaction fee is 0.3% of the winning payoff. In addition, InTrade charges 10 cents per contract on expiry (if you “win”). That’s another 1.0%.

So, when the market was quoting 97.8% likelihood of the HCR bill passing before June 2010, this didn’t really mean that there was a 2.2% chance of the bill not passing. A winning ticket would be subject to 1.3% transaction fees. The real likelihood of failure was 0.9% – approximating the uncertainty that Obama would be “hit by a bus” before signing the bill into law.

No rational investor would wish to purchase a share for more than 98.7, given the transaction costs. In a sense, this is the market’s “100%”. Interestingly, at 1:49pm GMT today (March 23), there are 695 bids at 99.1 and 413 asks at 99.2. Clearly, some traders are not subject to the full transaction fees at InTrade. More about that here.

[Cross-posted from Toronto Prediction Market Blog.]

1. Joe should mention whether there is volume on each market.
2. Joe should cite BetFair, not InTrade, for any UK-related event.
3. Joe should be aware of InTrade’s long history of fucking up contracts and settlements on non-sporting events. (Type “North Korea missile InTrade” in Google, and review the various InTrade forums for traces of past fights.)

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