To very briefly summarize Hayek's two most important ideas, he argued that socialism can't work as an effective system for producing and distributing goods because it has no way of aggregating the necessary information about people's wants and needs. By contrast, the price system of the market is a very effective method for collecting and using information about people's preferences and the relative value of different goods. Hayek's 1945 article "The Use of Knowledge in Society" is the best short statement of this argument. Hayek also argued that government control of the economy under socialism necessarily leads to the destruction of democracy and personal freedom. The central planners' control of the economy enables them to crush potential opposition and strangle civil society. This, of course, was the main argument of Hayek's most famous book, The Road to Serfdom (1944).It is clear from what he has written that Mr. Somin has read Hayek rather extensively and to good effect. There is plenty more worth reading in his original post.
Today's advocates of government planning are more modest in their ambitions than the mid-twentieth century socialists whom Hayek criticized. But they are not modest enough to make his arguments irrelevant.
I don't claim that Hayek was right about everything or that he perfectly foresaw our situation today. To the contrary, he made his share of mistakes. But his most important arguments haven't lost their relevance.
By coincidence I recently found this interview with Bruce Caldwell author of an intellectual biography titled Hayek's Challenge, also cited here. Here they are discussing The Road to Serfdom.
Kokai: This book is still influential more than 60 years after its publication. Do you think it is still going to have some influence 60 years from now?And so the disagreements between advocates of some form of ordered liberty and those advocating some form of statism go on and on and on!
Caldwell: I don’t think the basic human desire to control social phenomena, control society through social policy, is ever going to dissipate. And, in fact, I think it is a noble desire. I think that Hayek, though, points out certain problems that people encounter when they try to plan a society. So I think that message is one that we would forget only at our peril. I’ll just put it that way.