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In prediction markets, the fact that the weights of yes and no sum to 1 may seem unrelated to Hayek at first glance. But if you've read "The Use of Knowledge in Society," you'll realize that this guy actually pointed out the most fundamental problem in economics—the real challenge for society is not how to allocate resources, but how to aggregate the dispersed knowledge held by each individual.
The mechanism of prediction markets is essentially doing this. The probability distribution of yes and no is, in simple terms, integrating the judgments, information, and intuition of market participants into a single price signal. This process, in a sense, is answering the core question posed by Hayek—how to effectively utilize dispersed knowledge through mechanisms without central planning. It's quite interesting to think about: a century-old economic theory has now become the underlying logic for designing prediction markets.