The same quantity described as well below 1 also applies to wars, so forecasts for tail events in conflicts are not compatible with probability theory.

Judge as of 2023. True: empirical estimates of the tail index (alpha) of war casualties, e.g. Cirillo & Taleb 2016 (about 0.4 to 0.6) and independent studies, place it well below 1, as for pandemics. Mostly true: estimates are below 1 but around 0.7 to 0.9, or are below 1 only under some specifications. Mixed: estimates are split, with some below 1 and others around or above 1 (e.g. Clauset's war-size estimates, depending on whether casualties are rescaled to population). Mostly false: most independent estimates put alpha around or above 1, with only Taleb's own work finding it well below 1. False: estimates consistently put alpha clearly above 1.

Set before the research began.

1. E1 On the statistical properties and tail risk of violent conflicts arXiv (Cirillo & Taleb; page text lists no authors, but the bibliography of the ar5iv Clauset page cites this paper as Cirillo and Taleb 2015, Physica A 429) · 31 January 2026 Own record

   “In all cases, \(\xi\) is significantly greater than 1, and around 1.5 as we guessed by looking at Figure 10. This means that in all cases the mean of the distribution of casualties seems to be infinite”

2. E2 War Size Distribution: Empirical Regularities Behind the Conflicts Munich Personal RePEc Archive (working paper by Rafael González-Val, Universidad de Zaragoza) · August 2014

   “The estimated Pareto exponent is always less than 1, indicating that the distribution is heavy-tailed; this means that the war average loss is controlled by the largest conflicts.”

3. E3 How bad could a war get? Effective Altruism Forum (post by poppinfresh and rani_martin) · 4 November 2022

   “range from 1.35 to 1.74, with a mean of 1.60”

4. E4 On the frequency and severity of interstate wars ar5iv (arXiv 1901.05086; Clauset)

   “Using standard techniques to estimate \(\alpha\) and \(x_{\min}\), and to test the fitted distribution Clauset et al. 2009, we find that the set of observed interstate wars sizes, from 1823–2003, are statistically indistinguishable from an iid draw from a power-law distribution”

Among independent sources, only E2 gives an exponent with a stated meaning, and it is below 1. E3's figures of 1.35 to 1.74 do not say in the excerpt what they measure or which convention they use, and E4 gives no exponent, so the evidence does not show the split the 'mixed' verdict needs or settle any other category under the criteria.