Pinker's response is shall we say interesting, first he says:
The book does not claim that the mean of the distribution of war deaths has changed; it explicitly notes that power-law distributions (such as those commonly fitted to war deaths) don’t have calculable means. Like Taleb, the book points out that empirically observed data from the tail of a power-law distribution provide unreliable evidence for its underlying parameters.
He than proceeds to demonstrate that he doesn't in fact understand the implications of these statistics by writing stuff like this:
Finally, Taleb thinks that it is damning that “You can look at the data he presents and actually see a rise in war effects, comparing pre-1914 to post 1914.” Yes, that’s exactly what I point out: great-power wars became steadily more destructive from 1500 through 1945. The turning point that marks the onset the Long Peace was in 1945, not 1914.
A power law distribution means that at any given time not during a major war it looks like war has fallen to unprecedented levels.
A hypothetical proto-Pinker writing in 1913 could similarly note that the turning point was in 1814, possibly even citing the Franco-Prussian war to show how wars between great powers are now short and limited.
Not disagreeing, but I repeat that the hypothesis that 1945/1953 represent turning points is not unreasonable. and should be tested directly.
There's a new paper arguing, contra Pinker, that the world is not getting more peaceful:
On the tail risk of violent conflict and its underestimation
Pasquale Cirillo and Nassim Nicholas Taleb
Every claim in the abstract is supported by the data - with the exception of the last claim. Which is the important one, as it's the only one really contradicting the "long peace" thesis.
Most of the paper is an analysis of trends in peace and war that establish that what we see throughout conflict history is consistent with a memoryless powerlaw process whose mean we underestimate from the sample. That is useful and interesting.
However, the paper does not compare the hypothesis that the world is getting peaceful with the alternative hypothesis that it's business as usual. Note that it's not cherry-picking to suggest that the world might be getting more peaceful since 1945 (or 1953). We've had the development of nuclear weapons, the creation of the UN, and the complete end of direct great power wars (a rather unprecedented development). It would be good to test this hypothesis; unfortunately this paper, while informative, does not do so.
The only part of the analysis that could be applied here is the claim that:
This could mean that the peace since the second world war is not unusual, but could be quite typical. But this ignores the "per capita" aspect of violence: the more people, the more deadly events we expect at same per capita violence. Since the current population is so much larger than it's ever been, the average time delay is certainly lower that 101.58 years. They do have a per capita average time delay - table III. Though this seems to predict events with 10 million casualties (per 7.2 billion people) every 37 years or so. That's 3.3 million casualties just after WW2, rising to 10 million today. This has never happened so far (unless one accepts the highest death toll estimate of the Korean war; as usual, it is unclear whether 1945 or 1953 was the real transition).
This does not prove that the "long peace" is right, but at least shows the paper has failed to prove it wrong.