By 'order' we shall throughout describe a state of affairs in which a multiplicity of elements of various kinds are so related to each other that we may learn from our acquaintance with some spatial or temporal part of the whole to form correct expectations concerning the rest, or at least expectations which have a good chance of proving correct.
This definition of order is supposed to rule out chaotic systems like gas in a box or a climate. In such chaotic systems, local interactions do not necessarily give you information about global properties of the system. The bumping of two molecules together does not tell me anything about the overall density of a gas in a box. The weather in Calcutta does not tell me anything about the weather in La Paz.
A natural interpretation of Hayek's definition of order as applied to an economy might be something like this: a local interaction (say, exchange of money for a good) tells us something about global properties of the system (say, the marginal exchange rate of that good). This relationship between local and global properties depends upon the equilibria which develop in economic systems. Because local interactions produce global equilibria, I can learn about such equilibria from the local interactions in which I participate.
However, there is a problem here. Hayek has attempted to define a property internal to the system (its degree of order) in terms of the epistemic access of some agent interacting with the system. This definitional strategy does not (cannot?) take into account an important property of information: information is profligate—information is never monogamous!
What this means is simply that a local interaction contains information about an arbitrarily large number of complicating factors. The agent, attempting to derive "correct expectations" about the rest of the system has no principled way to determine which factors are potentially relevant to his local interaction.
Consider, for example, the case of beer in airports. On average in the U.S., the price of beer in airports is about double that in a regular street bar. If I walk into an airport bar and purchase a beer, the information I receive is qualitatively different from that I receive if I walk into my neighborhood dive bar. The transaction in the dive bar tells me something about the global marginal exchange rate of beer. The transaction in the airport bar tells me something about the marginal exchange rate of beer in airports. But how do I know that the fact that I am in an airport is relevant? We are trying to understand the informational content of a local interaction—how do I even know that I am in an airport?
Both the determination that I am in an airport and the determination that, in this case, the location of my exchange is relevant to the global information I receive from my transaction depend crucially on background knowledge. However, background knowledge is a property of the agent, not the system itself. So, Hayek's definition seems deficient in its attempt to define a property of the system in terms of the epistemological access of a potential agent.
Consider a final example: local beer in a Turkish airport costs roughly the same as local beer in an American airport. Now, suppose I am an American businessman traveling to the Middle East and I have a brief stopover in Turkey. I only see the inside of an airport and during my stopover I purchase a beer at an airport bar. What do I learn? On the basis of my background knowledge, I might deduce that the price of booze in Turkey is roughly that of booze in the U.S. This deduction makes sense on the assumption that the relationship between the cost of airport beer and everyday bar beer is the same in both countries.
However, I would be completely incorrect! As it turns out, the price of local beer at everyday bars in Turkey is about a third that of beer at everyday bars in the U.S. So, on the one hand, I have grossly overestimated the cost of beer in Turkey. On the other hand, the cost of hard liquor, since it is mostly imported, is approximately twice that in the U.S.—by generalizing to all booze, I have gone wrong again. Both assumptions (based reasonably on my background knowledge)—that beer in airports is twice that in an ordinary bar, and that the relative price of different types of booze tracks that in the U.S.—were in error. Again, if an agent's epistemic access is built into the definition, then the informational property defined is inherently relative to the agent's background knowledge and cannot distinguish a property purely internal to the system.