If you believe that markets are the most efficient way to allocate resources, what if their breadth was extended to be far beyond how they're used today? Posner and Weyl play with this concept, and deliver proposals outside the current political axis, leaving people of nearly every political persuasion both interested and aghast.
I'll focus on the proposal they get the most attention for, regarding property ownership. They offer an economic system that would implement a wealth tax, levied on all personal property valued at whatever you publicly declare its value to be. Except, anyone can immediately take ownership of anything of yours by exceeding your named price. This incentivizes accurate valuations, and encourages the optimal use of resources. If you undervalue property because you're underutilizing it, someone else can quite easily arbitrage this spread.
This is one of four radical ideas they present using markets. The others involve voting, immigration, corporate control, and data ownership.
Here's the generous interpretation: their book is an interesting philosophy of economics, rather than literal ideas that could be adopted wholesale. That interpretation fueled many interesting hypothetical discussions I've had recently. However, for me—a fairly layperson—there's significant flaws with many of them, but they're interesting to think about and guide how we build our future.