what the chances are that World War III will occur this
century.
Prof. Michael Spagat wrote that nobody knows, nobody can
really answer–and we totally agree with him on this. Then
he adds that "a really huge war is possible but, in my view,
extremely unlikely." To support his statement, Prof. Spagat
relies partly on the popular science work of Prof. Steven
Pinker, expressed in The Better Angels of our Nature and
journalistic venues. Prof. Pinker claims that the world has
experienced a long-term decline in violence, suggesting a
structural change in the level of belligerence of humanity.
It is unfortunate that Prof. Spagat, in his answer, refers to
our paper [1], which is part of a more ambitious project we
are working on related to fat-tailed variables.
What characterizes fat tailed variables? They have their
properties (such as the mean) dominated by extreme events,
those "in the tails". The most popularly known version is the
"Pareto 80/20".
We show that, simply, data do not support the idea of a
structural change in human belligerence. So Prof. Spagat’s
first error is to misread our claim: we are making neither
pessimistic nor optimistic declarations: we just believe that
statisticians should abide by the foundations of statistical
theory and avoid telling data what to say.
Let us go back to first principles.
Foundational Principles
Fundamentally, statistics is about ensuring people do not
build scientific theories from hot air, that is without significant
departure from random. Otherwise, it is patently "fooled by
randomness".
Further, for fat tailed variables, the conventional mechanism
of the law of large numbers is considerably slower and
significance requires more data and longer periods. Ironically,
there are claims that can be done on little data: inference is
asymmetric under fat-tailed domains.
We require more data
to assert that there are no black swans than to assert that
there are black swans
hence we would need much more data
to claim a drop in violence than to claim a rise in it [2].
Finally, statements that are not deemed statistically signifi-
cant –and shown to be so –should never be used to construct
scientific theories.
These foundational principles are often missed because,
typically, social scientists’ statistical training is limited to
mechanistic tools from thin tailed domains [2]. In physics,
one can often claim evidence from small data sets, bypassing
standard statistical methodologies, simply because the variance
for these variables is low. The higher the variance, the more
data one needs to make statistical claims. For fat-tails, the
variance is typically high and underestimated in past data.
The second –more serious –error Spagat and Pinker made
is to believe that tail events and the mean are somehow
different animals, not realizing that the mean includes these tail
events.
For fat-tailed variables, the mean is almost entirely
determined by extremes. If you are uncertain about the tails,
then you are uncertain about the mean
. It is thus incoherent
to say that violence has dropped but maybe not the risk of
tail events; it would be like saying that someone is "extremely
virtuous except during the school shooting episode when he
killed 30 students".
Robustness
Our study tried to draw the most robust statistical picture of
violence, relying on methods from extreme value theory and
statistical methods adapted to fat tails. We also put robustness
checks to deal with the imperfection of data collected some
thousand years ago: our results need to hold even if a third
(or more) of the data were wrong.
Inter-arrival times
We show that the inter-arrival times among major conflicts
are extremely long, and consistent with a homogenous Poisson
process: therefore no specific trend can be established: we as
humans can not be deemed as less belligerent than usual. For a
conflict generating at least 10 million casualties, an event less
bloody than WW1 or WW2, the waiting time is on average
136 years, with a mean absolute deviation of 267 (or 52 years
and 61 deviations for data rescaled to today’s population). The
seventy years of what is called the "Long Peace" are clearly
not enough to state much about the possibility of WW3 in the
near future.
Underestimation of the mean
We also found that the average violence observed in the
past underestimates the true statistical average by at least half.
Why? Consider that about 90-97% of the observations fall
below the mean, which requires some corrections with the
help of extreme value theory. (Under extreme fat tails, the
statistical mean can be closer to the past maximum observation
than sample average.)
A common mistake
Similar mistakes have been made in the past. In 1860, one
H.T. Buckle used the same unstatistical reasoning as Pinker
and Spagat.
REAL WORLD RISK INSTITUTE WORKING PAPER SERIES
2
That this barbarous pursuit is, in the progress
of society, steadily declining, must be evident, even
to the most hasty reader of European history. If we
compare one country with another, we shall find that
for a very long period wars have been becoming
less frequent; and now so clearly is the movement
marked, that, until the late commencement of hos-
tilities, we had remained at peace for nearly forty
years: a circumstance unparalleled (...) The question
arises, as to what share our moral feelings have had
in bringing about this great improvement.