The war file

Fact Richardson, 1960 — the founding dataset. Lewis Fry Richardson spent decades counting what he called deadly quarrels: every violent conflict he could document from 1809 to 1949 (the dyadic version of the dataset runs to 779 of them), each graded by magnitude — the base-10 logarithm of its death toll. Published posthumously (he died in 1953), the book carries the founding observation of this whole field, extending his 1948 paper on how the frequency of fatal quarrels varies with magnitude: quarrel frequency falls away with magnitude in a regular, power-law-like fashion. Small quarrels are common; giant ones are rare — but not nearly rare enough. Every party to the dispute below traces its lineage here: the Correlates of War project’s own history page names Richardson among the pioneers it built on, Pinker’s reply credits his pioneering conflict statistics, and Cirillo & Taleb’s reference list cites both the 1948 paper and this book.

Lewis Fry Richardson, Statistics of Deadly Quarrels, eds. Quincy Wright and C. C. Lienau (Pittsburgh: Boxwood Press, 1960; co-issued by Quadrangle Books, Chicago — either imprint appears in citations).

Fact The Correlates of War data — the common evidence. Founded in 1963 by J. David Singer at the University of Michigan, soon joined by the historian Melvin Small, the Correlates of War Project maintains the standard quantitative datasets on war and interstate conflict — war data, militarized interstate disputes, national material capabilities, state system membership — documented, replicable, and freely released. Singer & Small’s The Wages of War (1972) fixed the operational definition of war still in use. This is the shared evidentiary ground of the fight: Clauset’s 2018 referee paper runs on COW interstate wars, and both camps draw on it.

The Correlates of War Project, correlatesofwar.org.

Fact Cirillo & Taleb, 2016 — the tail, measured. The mint chip covers what they published, not who is right — that is the next section’s fight. From 565 armed conflicts with more than 3,000 casualties each, spanning two millennia (1–2015 CE), they fit generalized Pareto tails to war casualties and report a shape parameter ξ of about 1.5 — their maximum-likelihood estimates run from 1.4985 (raw data, 25k-casualty threshold) through 1.5868 (rescaled, 145k) to 1.5915 (dual, 145k), each significantly above 1, with their Pickands-plot reading also landing near 1.5. On their estimate that puts the tail exponent α = 1/ξ near 0.67, below 1: the naive distribution behaves as if its mean were infinite. Their bounded-support (dual) transform recovers a finite shadow mean — about 3.69×10⁷ casualties for rescaled data at the 145k threshold, against a sample mean of 1.77×10⁷ — so on their arithmetic the plain historical average understates the tail-adjusted mean by a factor of at least 1.6, and possibly up to about 7.5. They also find the arrival times of the largest wars consistent with a homogeneous Poisson process — no clustering, no drift: conflicts above 5 million dead arrive with a mean gap of 93.03 years (mean absolute deviation 113.57); above 10 million, 133.08 years raw, or 52.23 once the record is rescaled to today’s population.

Their stated conclusion cuts both ways, and the file reports both edges: sixty years without a 5-million-death war is, in their judgment, far too little evidence to conclude that such wars have become less likely — and, in the same breath, the data as they read them neither support nor refute a structural change in violence. A persuasive theory of more peaceful days may yet be built, they allow; it just cannot rest on this statistical analysis. Their abstract sets every statistical picture they obtain against the prevailing long-peace claims.

Pasquale Cirillo and Nassim Nicholas Taleb, “On the statistical properties and tail risk of violent conflicts”, Physica A: Statistical Mechanics and its Applications 452 (2016), 29–45, doi:10.1016/j.physa.2016.01.050; preprint arXiv:1505.04722.

Fact Pinker, 2011 — the thesis, stated so he would accept it. The Better Angels of Our Nature argues that rates of violence of many distinct kinds — homicide, torture and cruel punishment, slavery, war deaths per capita, civil war, terrorism, abuse of women, children and animals — have declined over multiple historical timescales: millennia, centuries, decades. Each decline, on his account, was driven by identifiable historical forces — states, commerce, feminization, cosmopolitanism, reason — engaging what the book calls our better angels against our inner demons. The post-1945 Long Peace among great powers is one of six distinct declines the book describes, not the whole thesis. And by his own account of this dispute, the book’s statistics do little more than describe past rates and their causes; it is not a guarantee that big wars are over — a point he says the book makes explicitly, and more than once.

Steven Pinker, The Better Angels of Our Nature: Why Violence Has Declined (New York: Viking, 2011; paperback Penguin Books, 2012).

Contested What is actually contested is narrower than the headlines, and sharper. Three things. Trend inference under fat tails: whether a few centuries of data — let alone seventy quiet years — can statistically distinguish a genuine decline from an ordinary lull in an unchanged fat-tailed process. Normalization: whether the right object is per-capita rates, which can fall as populations grow even while absolute tolls do not, or absolute severity, the quantity tail-risk arguments are usually stated in — Cirillo & Taleb run their own tables both raw and rescaled to today’s population; the fight is over which version the word decline is allowed to point at. Conflict definitions: where one war ends and another begins, what casualty threshold admits an event to the record — coding choices that can move the answer.

Contested The charge — Taleb & Cirillo, at their strongest. Under tails this fat, the law of large numbers works too slowly for seventy years of peace to carry real statistical information; showing that black swans are absent, they argue, takes far more data than showing they are present. On the arithmetic of their popular-form note, a war of ten million dead or more has an average waiting time of 136 years, with a mean absolute deviation of 267 — 52 years and 61 of deviation when the record is rescaled to today’s population (their Physica A paper prints the neighbouring figure, 133.08 raw). Seven post-war decades are therefore, on their reading, far too short an interval to say much about the near-term possibility of a third world war. The historical record, they add, understates violence’s true mean — by at least half, per their shadow-mean calculation. And they insist they forecast nothing, dark or bright: the claim is only that the decline-of-violence thesis has no statistical basis. Their Nobel Symposium paper states it at full strength — on their reading the long-peace and drop-in-violence theses rest on naive methodology, and the data give no statistical ground for saying times have changed; no ground, even, for talk of a trend.

Pasquale Cirillo and Nassim Nicholas Taleb, “What are the chances of a third world war?” (Real World Risk Institute working paper; published in Significance, 2016), bundled at that address with the full arXiv:1505.04722 preprint; and “The Decline of Violent Conflicts: What Do The Data Really Say?”, Nobel Foundation Symposium 161: The Causes of Peace (2016), hosted at fooledbyrandomness.com/pinker.pdf.

Claim A note on the paper trail. The opening shot was a 2012 note by Taleb titled “The ‘Long Peace’ is a Statistical Illusion”. Its original text is no longer served at its old address — the title survives, attested verbatim in Pinker’s reply — and that address today carries the argument’s live 2016 form instead, cited above. This file paraphrases only the live documents; nothing here leans on the vanished one.

Contested The reply — Pinker, at his strongest. His answer is titled, in full, “Fooled by Belligerence: Comments on Nassim Taleb’s ‘The Long Peace is a Statistical Illusion’”. Five moves, paraphrased from the document itself. One: the charge attacks a misreading — the book’s statistics are descriptive graphs of past rates, they extrapolate nothing, and the book denies explicitly and repeatedly that major violent shocks are ruled out for the future. Two: the Long Peace — John Gaddis’s term — refers specifically to the post-1945 fall of war among great powers and developed states to depths the record had not shown before: a report about the past, not a forecast, and one of six distinct declines governed by very different statistical processes. Three: the book already makes Taleb’s own points — power-law war magnitudes without calculable means, unreliable tail estimates, survivorship bias, historians over-reading trends — in a chapter that, he remarks, might as well have borrowed a title from Taleb’s own shelf. Four: against the illusion hypothesis he stacks multiple independent indicators, noted prospectively rather than fitted after the fact — war among developed states dropping essentially to zero, territorial conquest vanishing, conscription and service terms and per-GDP military spending cut hard, declines in every exogenous variable that statistically predicts militarized disputes, war disappearing as a live policy option — suggesting a qualitative change, while conceding that none of it proves the probability has fallen; the past guarantees nothing. Five: the genuine concessions — no lower bound on the probability of a catastrophic war, no upper bound on its damage; agreement that the expected damage of future conflict cannot be compressed into a single number; both the chance of war is lower and the worst imaginable war is worse can be true at once, which is why the book never claims the world is safer across the board — and Taleb is right, he grants, to keep eyes on tail magnitudes, though guarding against every imaginable catastrophe has costs of its own.

Steven Pinker, “Fooled by Belligerence: Comments on Nassim Taleb’s ‘The Long Peace is a Statistical Illusion’” (circulated November 2012), self-hosted PDF, stevenpinker.com.

Fact Clauset, 2018 — the wait-time number. Aaron Clauset took the Correlates of War interstate record (1823–2003) and asked the dispute’s question directly: is the post-1945 peace statistically surprising? Running realistic but stationary models of conflict generation — models in which nothing about war has changed — he found that both the long peace and the preceding storm of 1914–45 sit comfortably inside what such an unchanged process produces. His number, as verified: on his arithmetic, statistical significance for the post-war peace lies at least another 100 to 140 years away. He adds that this does not make the long peace unimportant — only that it may be far more fragile than its proponents take it to be.

Aaron Clauset, “Trends and fluctuations in the severity of interstate wars”, Science Advances 4(2), eaao3580 (21 February 2018), doi:10.1126/sciadv.aao3580 — open-access full text at PMC.

Fact Braumoeller, 2019 — the persistence thesis. Bear Braumoeller’s Only the Dead reads the same record and concludes that the data do not support the decline-of-war thesis: rates of conflict initiation have not declined since 1816, the distribution of war severities remains as deadly as it ever was, and such peace as exists is manufactured — the product of international orders, shared sets of expectations that let states act in concert (the Concert of Europe is his model case) — not of any softening in human bellicosity.

Bear F. Braumoeller, Only the Dead: The Persistence of War in the Modern Age (New York: Oxford University Press, 2019) — thesis as summarized in Michael Spagat’s book note, Journal of Peace Research.

The seam — a synthesis, ungraded on purpose: check it against the graded cards above. Nobody in this fight disputes that the dead are real, and the datasets — Richardson’s quarrels, the Correlates of War tables — are the ground both camps walk on, though individual tolls carry the wide error bars and coding fights noted above. Nor is the fat tail itself in dispute: Richardson observed it, Cirillo & Taleb measured ξ near 1.5, Pinker’s book teaches the same power-law point by his own account, Clauset’s stationary models run on the same Correlates of War record, and Braumoeller finds the distribution of war severities as deadly as it ever was. The sharpest part of the fight is over what a trend claim is allowed to mean when the tail is that heavy — how long a quiet stretch must run before quiet is evidence of change rather than an ordinary silence between rare, giant events.

The wing already holds this dispute in toy form: the lying average is this fight, miniaturized — a sample mean under fat tails keeps promising a number it cannot yet deliver, for precisely the reason seventy years of peace may carry less information than they seem to. Same theorem, stakes turned all the way up. This page sells no verdict on who wins; the fence holds.