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.
The simplest power law , a*x^k has two parameters which govern the overall location and the fatness of tails, I think. You could expect a change in either or both. So you could fit a time-series model in which a and k can change each year by an amount drawn from a distribution, and then see whether the data supports a large net change since 1945? This is what I take Stuart as suggesting.
The available data must support some range of ks, some precision, and if allowing any shift of k over time indicates that k has fallen a lot lately, that’s pretty bad for their theory. If they say you should ignore the data, then they’re doing theology.
If the range of ks is large then the posterior probability of a shift (or to put it another way, the estimated probability that pre-WWII ks differ from post-WWII ks) will be appropriately small and Taleb will have demonstrated what he wants to demonstrate without so much rhetoric and an analysis that largely misses the point.
Pinker’s response is shall we say interesting, first he says:
He than proceeds to demonstrate that he doesn’t in fact understand the implications of these statistics by writing stuff like this:
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.
What does “turning point” mean in the context of a power law distribution?
The simplest power law , a*x^k has two parameters which govern the overall location and the fatness of tails, I think. You could expect a change in either or both. So you could fit a time-series model in which a and k can change each year by an amount drawn from a distribution, and then see whether the data supports a large net change since 1945? This is what I take Stuart as suggesting.
The problem is that you can’t estimate ‘k’ well enough, at least that’s what Taleb argues at various places.
The available data must support some range of ks, some precision, and if allowing any shift of k over time indicates that k has fallen a lot lately, that’s pretty bad for their theory. If they say you should ignore the data, then they’re doing theology.
The point is range of ks is quite large. That’s what Taleb’s work as a professor of Risk Engineering is about.
If the range of ks is large then the posterior probability of a shift (or to put it another way, the estimated probability that pre-WWII ks differ from post-WWII ks) will be appropriately small and Taleb will have demonstrated what he wants to demonstrate without so much rhetoric and an analysis that largely misses the point.