Abstract
Since 1945, there have been relatively few large interstate wars, especially compared to the preceding 30 years, which included both World Wars. This pattern, sometimes called the long peace, is highly controversial. Does it represent an enduring trend caused by a genuine change in the underlying conflict-generating processes? Or is it consistent with a highly variable but otherwise stable system of conflict? Using the empirical distributions of interstate war sizes and onset times from 1823 to 2003, we parameterize stationary models of conflict generation that can distinguish trends from statistical fluctuations in the statistics of war. These models indicate that both the long peace and the period of great violence that preceded it are not statistically uncommon patterns in realistic but stationary conflict time series. This fact does not detract from the importance of the long peace or the proposed mechanisms that explain it. However, the models indicate that the postwar pattern of peace would need to endure at least another 100 to 140 years to become a statistically significant trend. This fact places an implicit upper bound on the magnitude of any change in the true likelihood of a large war after the end of the Second World War. The historical patterns of war thus seem to imply that the long peace may be substantially more fragile than proponents believe, despite recent efforts to identify mechanisms that reduce the likelihood of interstate wars.
Fig. 1 The Correlates of War interstate war data (30) as a conflict time series, showing both severity (battle deaths) and onset year for the 95 conflicts in the period 1823–2003.
Fig. 2 Interstate wars sizes, 1823–2003.The maximum likelihood power-law model of the largest-severity wars (solid line, αα^ = 1.53 ± 0.07 for x=x^min=7061) is a plausible data-generating process of the empirical severities (Monte Carlo, pKS = 0.78 ± 0.03). For reference, distribution quartiles are marked by vertical dashed lines. Inset: Bootstrap distribution of maximum likelihood parameters Pr(αα^), with the empirical value (black line).
Fig. 3 Times between interstate war onsets, 1823–2003.The maximum likelihood geometric model (solid line, q^=0.428±0.002 for t ≥ 1) is a plausible data-generating process of the empirical delays (Monte Carlo, pKS = 0.13 ± 0.01), implying that the apparent discontinuity at t = 5 is a statistical artifact. Inset: Bootstrap distribution of maximum likelihood parameters Pr(q^), with the empirical estimate (black line).
Fig. 4 Cumulative counts of wars by general severity.(A) Empirical counts of wars of different sizes (dark lines) over time against ensembles of simulated counts from a stationary model, in which empirical severities are replaced iid with a bootstrap draw from the empirical severity distribution (model 1). For reference, dashed lines mark the end of the Second World War and the end of the Cold War. (B) For the largest-severity wars alone, empirical and simulated counts for three models of stationarity, which incorporate progressively more variability in the underlying data-generating process (see main text).
Fig. 5 How long must the peace last?(A) Simulated accumulation curves for wars of different sizes under a simple stationary model (model 1; see main text), overlaid by the empirical curves up to 2003 (dark lines) and linear extrapolations of the empirical postwar trends (the long peace) for the next 100 years (dashed lines). Quartile thresholds are derived from empirical severity data. (B) Fraction of simulated conflict time series that contain more large wars (x ≥ x0.75) than observed in the past or than expected in the future relative to a linear extrapolation of the postwar tend. Years at which the postwar trend (the long peace) becomes statistically unlikely under a stationary model, relative to 95% of simulated time series, are marked with open circles.
