On the deterrence effect of nuclear weapons, I think the following empirical finding is interesting. (Though not conclusive, as this kind of research design cannot establish causality.)
Sample (2000) found that arms races increase the chances of both MIDs [militarized interstate disputes] and the likelihood that an MID will escalate to full-scale war. However, she discovered that this was only the case in disputes that occurred before World War II. Similarly, territorial disputes were no longer found to be associated with escalation in the post–World War II era. Sample suggested that the presence of nuclear weapons was a possible explanation for why arms races in the post-war era were found to be less likely to result in the outbreak of war than those that occurred prior. She introduced a nuclear weapons variable to test this and found that the probability of war decreased to .05 when nuclear weapons were present during a mutual military buildup. Sample’s discovery of the potential pacifying effect of nuclear weapons was an important contribution to our understanding of how quantitative and qualitative arms race–war relationships differ.
Quote from Mitchell and Pickering, 2017, an encyclopedia article reviewing work on arms races (emphasis mine). On the impact of nukes, they continue (emphasis mine):
The advent of nuclear weapons thus appears to have changed the arms race–conflict relationship. It is important to note in this regard that many policymakers seem to place nuclear weapons in a different conceptual category than conventional weapons. As Sagan (1996, p. 55) has argued, nuclear weapons “are more than tools of national security; they are political objects of considerable importance in domestic debates and internal bureaucratic struggles and can also serve as international normative symbols of modernity and identity.” There have also been attempts to explain “nuclear reversal” cases by which states forgo or give up on their programs (Campbell et al., 2004; Levite, 2003; Paul, 2000; Reiss, 1995; Rublee, 2009). Research has shown that the possession of such weapons is contingent upon both willingness and opportunity (Jo & Gartzke, 2007). While security concerns and technological capabilities are significant determinants of whether states pursue the development of nuclear weapons, the possession of such weapons is dependent upon such factors as domestic politics and international considerations (Jo & Gartzke, 2007). Furthermore, states are heavily dependent upon sensitive nuclear assistance from more advanced nuclear states when attempting to develop a nuclear arsenal (Kroenig, 2009a, 2009b).2 The nature of nuclear weapons acquisition is thus multifaceted and may not always be motivated by arms races. Once acquired, however, nuclear capabilities seem to impact the likelihood of conflict escalation and disputes between states.
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[Gibler et al. 2005] controlled for several variables previously demonstrated to be predictors of conflict in a dyad. Among these was the joint presence of nuclear weapons, which was shown to prevent the outbreak of war (as no war has occurred in a dyad where both states possessed nuclear weapons). However, if both states had nuclear weapons, this was found to actually increase the probability of MID onset. Subsequent research has shown that nuclear dyads have engaged in a large number of militarized disputes short of war and may be even more likely to engage in MIDs than non-nuclear states or asymmetric pairs of states (see, e.g., Beardsley & Asal, 2009; Rauchhaus, 2009).
Gibler et al.’s (2005) discovery that nuclear dyads are less likely to engage in all-out war between rivals but more likely to engage in MIDs and hostile action short of war contributes to the broader understanding of the role nuclear weapons play in state decisions to use military force. Although a detailed discussion of nuclear deterrence is outside the scope of this article, it is important to highlight a key debate within this context. Among those who believe that nuclear weapons can serve as a deterrent (often referred to as “proliferation optimists”), some have argued that possession can deter aggression at all levels (Jervis, 1989; Waltz, 1990). Others, meanwhile, have contested that possession secures states from high-level conflict escalation (e.g., war) but increasingly contributes to lower-level hostile action (e.g., MIDs) (Snyder, 1965; Snyder & Diesing, 1977). This concept is known as the “stability-instability paradox,” which states that “to the extent that the military balance is stable at the level of all-out nuclear war, it will become less stable at lower levels of violence” (Jervis, 1984, p. 31).
On the deterrence effect of nuclear weapons, I think the following empirical finding is interesting. (Though not conclusive, as this kind of research design cannot establish causality.)
Quote from Mitchell and Pickering, 2017, an encyclopedia article reviewing work on arms races (emphasis mine). On the impact of nukes, they continue (emphasis mine):