The Obama Administration, like some in the Bush Administration before it, seems convinced that, at the end of the day, China and Russia will help constrain Iran’s game-changing nuclear weapons ambitions. The thinking is that Beijing and Moscow, as permanent members of the UN Security Council with large economies and global presence, are more “with us” as benefactors of the global power status quo than “against us” as disruptors of it. But is this truly the case? After wheedling useful offers from Washington as American diplomats try to secure Chinese and Russian support for sanctions against Iran, will these two powers now see their fundamental national interests aligned with the United States? Do U.S. officials even understand the fundamental national interests of Moscow and Beijing, let alone Tehran, and do we know how they go about promoting those interests?

Although China, Russia and Iran are not members of some new “axis of evil”, it is not off the mark to think of them, under their current leaderships, as part of an authoritarian rotary, or a group of governments that share similar strategic outlooks and know-how to invest broadly and creatively in their own long-term advantage. They are not allies, but they do share a certain body language, which gives them a mild affinity for one another. They know, too, that the United States doesn’t speak that language and shares no such affinity.

The strategic cultures of China, Russia and Iran are all deeply rooted in their specific historical narratives, but they nonetheless share striking similarities. Each narrative runs the gamut from glory to ignominy. Each remembers a time when its empire was vast and its culture widespread. Yet each recalls humiliations suffered at the hands of foreigners, sometimes aided by internal dissidents, who exploited internal instability to end an empire. The two quests spawned from these narratives—to reclaim past glory and to guard against future humiliation—are ubiquitous in these countries’ strategic writings, and they influence how their current leaderships act in the world and in relation to the United States.

China, Russia and Iran also share the authoritarian’s luxury of having at hand all the tools of both the public and private spheres. (Indeed, they often see little distinction between these spheres.) They also have an easier time shunting aside civil rights and political liberties and so have a relatively easy time using all sources of power to pursue foreign policy goals. As the U.S. government subjects itself to one review after another tasked with creating “whole of government” approaches to a raft of complex challenges, Beijing, Moscow and Tehran have been practicing that art for centuries. They have deftly recruited new associates and affiliates into the rotary, whether...