How would realist, liberal, and constructivist international relations scholars agree and disagree on how deterrence works? 

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In discussions involving realist, liberal, and constructivist theories of international relations in general and deterrence in particular there is a tendency of many scholars to oversimplify schools of thought, and an equally marked tendency to use “straw men” arguments, in which false assumptions are attributed to a particular school of thought for the purpose of debunking those arguments.  The most common oversimpliflication is that of the realist perspective, for which liberal and constructivist scholars ascribe to realists the notion that deterrence is purely a matter of rational calculations of self-interest and for which deterrence of an adversary is a product of a rational threat of retaliation.  As Richard Price and Nina Tannenwald wrote in their essay “Norms and Deterrence: The Nuclear and Chemical Weapons Taboo,”

“Deterrence has been invoked as the primary explanation for two central phenomena of twentieth-century international relations-the non-use of nuclear weapons and the non-use of chemical weapons. Yet, upon closer examination, it becomes clear that the conventional notion of deterrence-based on a rationalist account does not by itself adequately account for the practice of non-use of these weapons. Instead, a significant normative element must be taken into account in explaining why these weapons have remained unused.  Moreover, closer examination also reveals that rationalist explanations for the development of these norms themselves are indeterminate at best or mistaken at worst.”

As advocates of the constructivist approach argue, factors that do not lend themselves to simple calculations of self-interest in the face of threats of retaliation cannot alone account for decisions by governments to eschew the use of certain weapons, or for decisions to not invade another country. History and national values contribute to decisions to act or, conversely, to not act.  Realists no more deny the basic truth in that than liberals would deny that self-interest and power-politics play a role in some decisions.  The constructivist approach of threading the needle is entirely appropriate, but also goes too far itself in rejecting the traditional role of power-politics.

The liberal emphasis on collective security and arms control as pillars of deterrence does not account for the inherent weaknesses of collective security organizations in which decision-making is diffuse but actual capability is consolidated in one or two stronger member countries.  Both the liberal and the realist school can agree that deterrence predicated upon threats of massive retaliation are inherently immoral, but differ widely about ways to diminish that emphasis.  The liberal school is similar to the constructivist in its recognition of innumerable, sometimes hard to quantify variables, for example, a history of being invaded, and cultural influences like histories of racism.  All of these factors can influence a government’s approach to decision-making, and all can explain the successes or failures of deterrence.  The constructivist school, more than the realist or liberal schools, ascribes the function of deterrence more in “human” terms, in which, to quote Alexander Wendt, “structures of human association are determined primarily by shared ideas rather than material forces.”  In other words, man-made international structures are not, or need not be determinative of international relations.

No one school of thought pertaining to deterrence fits all situations; in virtually every case one can think of, multiple variables influenced decisions.  Examples of deterrence succeeding are more difficult to come by.  After all, it is rarely easy to definitively explain why something did not occur.