William C. Wohlforth is the Daniel Webster Professor at the Department of Government, Dartmouth College. Stephen Brooks is associate professor of government at Dartmouth College. The opinions expressed in this commentary belong to the authors.

(CNN) How would the United States fare without its globe-girdling array of military alliances? For the first time in memory, this is no longer an academic question.

President-elect Donald Trump has questioned why the United States invests so much in these security partnerships when it seemingly receives so little in return.

By either abandoning or neglecting commitments, or seeking to shake down allies for better deals, a Trump administration might lead us to a world without robust US security alliances -- the very foundation of the "globalist" American posture many Trump supporters disparage. And that would be an extremely high-risk gamble.

Our recent book, " America Abroad ," examines what a world without US alliances would look like; we conclude that a large-scale pullback would serve America's interests only if four assumptions are true.

More nuclear states

First, you have to believe that the spread of nuclear weapons will occur in a responsible way, with all the new nuclear weapons states building up the kinds of survivable forces that have little risk of accidents and miscalculations.

Make no mistake -- there will be many new nuclear states. Trump has mused that it might actually be good if allies currently under the US security umbrella were to seek nuclear deterrents. But proliferation would not stop there: Alarmed neighbors would almost certainly follow suit.

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Could we count on new nuclear powers to secure their forces, to make sure they do not get into the wrong hands and are subject to reliable control in a crisis? Reams of scholarship says no. To take one example: Pakistan has built what scholars say is a highly unstable hair-trigger nuclear arsenal, and is mainly responsible for proliferating nuclear capability to North Korea.

A world without US security guarantees risks more such states, with the attendant risks of nuclear war and leakage to hostile nonstate actors.

Arms races and risk of war

Second, you have to believe that decreased security abroad will not make the United States less secure. Removing US security guarantees clearly makes allies less secure, and that fear will drive arms races and risk war. Just think about what happens if we were to stop underwriting Japan's security -- given the historical animosities involved, what happens when Japan responds on its own to China's growing military power, how do Beijing and other regional powers react, and so on?

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Regions engulfed in rivalry, arms racing, crises and possibly armed conflict would escalate the challenges of dealing with the security problems of today while also generating new ones.

Think addressing threats such as ISIS and al Qaeda is hard now? Try dealing with those issues if Europe and Asia were also destabilized and themselves generating different and possibly even more challenging threats.

War costs everyone

Third, you have to believe that instability and war abroad will not affect prosperity at home. There is little doubt that war and instability "over there" would affect prosperity here. To believe otherwise, you have to believe that US firms and investors can somehow avoid being harmed by the turbulence in the markets that would inevitably follow conflicts overseas.

Academic studies debunk that belief for what it is: a relic of your grandfather's world economy (back when financial markets were not tied together in an elaborate web and when vast swaths of American firms were not highly reliant on overseas plants, research facilities and suppliers as they are now).

Alliances take hard work; why put that to waste?

Fourth, you have to believe that the United States can create coalitions on an ad hoc, as-needed basis. But alliances of the kind the United States now possesses can't just be assembled the moment Washington faces a crisis and wants help from other states.

US alliances are deeply institutionalized relationships, reflecting complicated bargains that cannot be reduced to a zero-sum "who gets what?" real estate transaction. Their construction in the early Cold War took immense efforts, and conditions were uniquely favorable: The United States produced some 40% of global output, Europe and Asia lay wrecked from the world war, and America and its partners faced the overpowering need to contain the threat of Soviet power.

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Consider, also, how few and unreliable Russia's and China's long-term allies are. Moscow can often depend on Belarus and it may have a loyal partner in Bashar al-Assad's Damascus. For its part, China has North Korea. Would they like to have more? Sure, but building up alliances is hard to do -- something to ponder before putting current US alliances on the chopping block.

To think that pulling back will go well for America requires confidence that many other important things would work out right: that global oil prices will always quickly stabilize if a conflict emerges in major oil-producing region; that maintaining the openness of the sea lanes will not be made more difficult and perilous; that abandoning alliances with the world's leading economies will not sap the US ability to prevent the global economic order it constructed after World War II from being changed in ways damaging to America's interests; that inter-state cooperation on all sorts of other issues, from terrorism to global crime to the environment, will work just as well without the leverage the United States gains from its alliances.

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Having reviewed the relevant scholarship, it's hard to find any basis for optimism on how these issues would pan out.

There are good reasons most national security experts condemned loose talk about US alliances being "obsolete": The world that would emerge in their absence would be much more dangerous.