Jason Smith in Evonomics:
Friedrich Hayek did have some insight into prices having something to do with information, but he got the details wrong and vastly understated the complexity of the system. He saw market prices aggregating information from events: a blueberry crop failure, a population boom, or speculation on crop yields. Price changes purportedly communicated knowledge about the state of the world.
However, Hayek was writing in a time before information theory. (Hayek’s The Use of Knowledge in Society was written in 1945, a just few years before Claude Shannon’s A Mathematical Theory of Communication in 1948.) Hayek thought a large amount of knowledge about biological or ecological systems, population, and social systems could be communicated by a single number: a price. Can you imagine the number of variables you’d need to describe crop failures, population booms, and market bubbles? Thousands? Millions? How many variables of information do you get from the price of blueberries? One. Hayek dreams of compressing a complex multidimensional space of possibilities that includes the state of the world and the states of mind of thousands or millions of agents into a single dimension (i.e. price), inevitably losing a great deal of information in the process.
Information theory was originally developed by Claude Shannon at Bell Labs to understand communication. His big insight was that you could understand communication over telephone wires mathematically if you focused not on what was being communicated in specific messages but rather on the complex multidimensional distributions of possible messages. A key requirement for a communication system to work in the presence of noise would be that it could faithfully transmit not just a given message, but rather any message drawn from the distribution. If you randomly generated thousands of messages from the distribution of possible messages, the distribution of generated messages would be an approximation to the actual distribution of messages. If you sent these messages over your noisy communication channel that met the requirement for faithful transmission, it would reproduce an informationally equivalent distribution of messages on the other end.
We’ll use Shannon’s insight about matching distributions on either side of a communication channel to match distributions of supply and demand on either side of market transactions.
More here.