After I blogged Cirillo and Taleb’s new paper on the long-term trend in war deaths, I read other commentaries on the debate (William Briggs, Dart-Throwing Chimp, STATS.org) and interacted with the authors. All that sharpened my thinking. Refinements:
- The paper is postured as a rejoinder to Steven Pinker. But I think if you are going use statistics to show that someone else is wrong, you should 1) state precisely what view you question, 2) provide examples of your opponent espousing this view, and 3) run statistical tests specified to test this view. Cirillo and Taleb skip the first two and hardly do the third. The “long peace” hypothesis is never precisely defined; Pinker’s work appears only in some orphan footnotes; the clear meaning of the “long peace”—a break with the past in 1945—is never directly tested for.
- Largely, the paper argues that the historical data do not appear improbable if we assume no trend over 2,000 years in war deaths. That is, the data are consistent with no trend. Pinker argues that the data are compatible with a decline, at least after 1945. But the first statement does not contradict the second. Normally competition between models is decided by fitting a single model that encompasses both, then testing whether a differentiating parameter, such as the coefficient on a post-1945 dummy, is statistically different from zero. As I explained last time, Cirillo and Taleb could do that with their models but don’t. So there is hardly any direct confrontation of the two theories.
- The cause for the modifier “hardly” is a single graph in the paper, Figure 8. Cirillo and Taleb check whether the average number of years between significant wars (those causing at least 50,000 deaths after rescaling to today’s population of 7.2 billion) exhibits serial correlation. If the gap between two such wars is short, should we expect the wait time for the next one (or the one after that, or the one after that…) to also be shorter? That would indicate time patterns in the frequency of significant wars. Cirillo and Taleb find no such correlation, looking as far ahead as the next 20 wars. (In my last post I incorrectly described this as next 20 years.) This is the sole reported basis for the assertion of no time trend.
My suspicion was that the averages of such correlations over 2014 years are a weak basis for detecting a long peace in the last 69. So I ran simulations, which appear to confirm this suspicion. The simulations assume that a significant war occurred on average once every 3 years until 1945, and once every 10 after. The Ljung-Box test based on the first 20 serial correlations is revealed as having no power to detect a “long peace.” But adding a post-1945 dummy to a model of the probabilistic process (a Poisson model) works very well.
- I guessed at one-in-three as the average war rate in the Cirillo and Taleb data set because they never report their sample size. I asked the authors about the true rate and offered to “tweak [the] simulation for realism.” Cirillo did not disclose the sample size and suggested I “wait until the final version of the paper, when data will be shared for everyone to check.” So for now, the advancement of the researchers appears to have trumped the advancement of research. Cirillo did seem to support the use of the Ljung-Box test.
- Taleb is comically arrogant. I am a “BSer” on whom Cirillo is “wasting your precious dinner time.” Apparently Taleb often behaves this way, so I shouldn’t feel special about the attention.
It looks as though Cirillo and Taleb have never checked for a trend break at 1945, even though that is the clear meaning of the “long peace” assertion they claim to challenge. Perhaps they see themselves as testing for some other pattern in the time domain. But that gets back to my first point: I can’t really tell what assertion they are challenging and who, if anyone, espouses it.