What do prediction market prices mean?

That's the question of the moment, brought up in a paper by Charles Manski, and highlit by Michael Stastny at both his guest gig at Marginal Revolution, and at his own pad Mahalanobis. Daniel Davies makes an interesting point on the way to disagreeing with the Manksi conclusion that the prices reported on the prediction markets are "not a meaningful measure of the central tendency of the distribution of beliefs, other than that the true average belief has to fall somewhere within fairly wide bounds of the market price, these bounds being determined by the distribution of the size of trading accounts," by examining the assumptions of the Manski model:

However, I think that the actual state of the world is somewhat better for the markets crowd than Manski’s paper suggests. As I see it, the engine of the paper is that it has two big assumptions, both of which I regard as unrealistic:

1) traders in the market are assumed to be price-takers
2) the distribution of account sizes is assumed to be independent of the distribution of beliefs.

I think that the first assumption is unreasonable as a characterisation of markets in general; it’s a sort of Arrow-Debreu world in which prices are arrived at by a process of tatonnement or sealed envelope auction, and then set “all at once” at a price that equates total supply to total demand. I personally think that this is sociologically an unrealistic characterisation of all market processes1 everywhere, a particularly bad way of describing securities markets in general2 and, importantly, factually wrong as a characterisation of the IEM.

1 Historically, it was this assumption which marked the big split between the Austrian economists and what was to become the neoclassical school. For an Austrian, abstracting from the actual things people do in a market to start talking about a frictionless abstraction of a market, is about the dumbest thing you can do. This is related to the point of Hayek scholarship I keep making; that markets are social institutions that (in my opinion, others differ) can’t be conjured out of thin air.

2 This view is now mainstream in economics; the field of “market microstructure” deals with the way in which the price discovery process works itself out in securities markets.

I've been meaning to link to Daniel's points on the Hayekian requirements of a market (that a market has to have both hedgers and speculators to work, and ultimately thus has to have a real world rationale for existing and cannot be conjured up just for speculation) but kept forgetting[3]. I think this goes to Patri's point about Hope vs. Belief somewhat- what people's beliefs are about the likelihood doesn't matter unless they are acted upon, and its the action (and interaction with others in the market) that "draw[s] out more beliefs and less hope", the latter being what I think Manski's proposed "distribution of beliefs" actually is. Daniel further points out:

And when you think about it, this stylised fact means that the size of your endowment or trading account can’t be independent of your beliefs. Assumption 2) was always unrealistic (it’s a feature of Manski’s model that there are no such things as weakly or strongly held beliefs; you just decide on your own fair value and buy units below that price), but in a world of limited liquidity, it’s simply unsustainable.


If Fatty thinks that the fair value of the contract is 55 or higher, he will spend his entire $500 endowment in Manski’s model. But if he only thinks the contract is worth 52, then the fact that his account is worth $500 is irrelevant; he’s only going to invest $100 @50 and $50 @51, so his account might as well only have been a $150 one. So I don’t think it makes sense to make the strong assumption that the size of trading accounts is independent of beliefs about fair price; people with extreme beliefs are going to be able to deploy big accounts but people with beliefs near the market aren’t.

Given the way the market seems to work, it would seem that Daniel's analysis is probably correct. I'd also think that big accounts and extreme positions would not be sustainable in the long view if they're too far from reality (though even such distortion would be information).

One last note:

fn3. I first saw it linked to by Brad DeLong, but Brad's archives are so byzantine that I could never find the post again, either by automatic or manual searching. Then Daniel mentioned it again a few weeks ago, but in the context of a post that I wished to take issue with, but never did, so again I forgot about my point... :idea:

Share this

There's some excellent

There's some excellent analysis of this here: