In chapter 7 of Fareed Zakaria's book The Post-American World, he lists six "new rules" ("guidelines") for how America should employ its power in the ever-changing geopolitical climate.
The first rule relates to choice. Zakaria argues that America can no longer get everything it demands from other countries. Now, it must choose where to "draw lines." This point looks valid, as it's what America's past two presidents have done. With countries like China and areas like the Middle East, Barack Obama and Donald Trump have embraced a selective approach.
The second guideline appears to align with the first rule. Zakaria writes that America should follow "broad rules, not narrow interests." This rule seems valid. As America must choose, it should promulgate rules that allow it to choose without lending itself to accusations of hypocrisy. For example, Zakaria argues that American shouldn't present itself as a champion of democratic movements across the world if it isn't prepared to choose to support democratic movements in countries like Saudi Arabia.
The third rule—"Be Bismarck not Britain"—is Zakaria's way of saying that America should communicate with all major powers. This rule ties into the next rule—"Order à la carte." These two rules could be called valid. America should maintain relationships with influential countries so that it has an array of options to solve the world's problems. The fifth rule—"Think asymmetrically"—appears valid, because it links to the previous guidelines that advocative flexible political action.
The final guideline—"Legitimacy is power"—might be up for debate. Zakaria's claim that the United States was once "loved, or at least liked" could strike some as suspicious. As historians like Howard Zinn and Roxanne Dunbar-Ortiz have shown, plenty of people never "liked" or "loved" America. The idea that America ever carried legitimacy seems based on a narrow interpretation of history that might be invalid.