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1
http://dx.doi.org/10.13140/RG.2.2.34461.00486/1
Contrary to the
statement in the
Royal Statistical
Society citation,
the figures
directly
comparing
numbers killed by
lawnmower with
those killed by
Jihadist terrorists,
do NOT ‘highlight
misunderstanding
s of risk’ or
‘illuminate the
bigger picture’.
They do the
exact opposite as
we explain here.
Are lawnmowers a greater
risk than terrorists?
Norman Fenton and Martin Neil, 3 January 2018
In December 2017 the Royal Statistical Society announced the
winner of its “International Statistic of the Year”. The citation1
announced it as follows:
WINNER: INTERNATIONAL STATISTIC OF THE YEAR
69
This is the annual number of Americans killed, on average,
by lawnmowers - compared to two Americans killed
annually, on average, by immigrant Jihadist terrorists.
The figure was highlighted in a viral tweet this year from Kim
Kardashian in response to a migrant ban proposed by President
Trump; it had originally appeared in a Richard Todd article for
the Huffington Post.
Todd’s statistics and Kardashian’s tweet successfully
highlighted the huge disparity between (i) the number of
Americans killed each year (on average) by ‘immigrant Islamic
Jihadist terrorists’ and (ii) the far higher average annual death
tolls among those ‘struck by lightning’, killed by ‘lawnmowers’,
and in particular ‘shot by other Americans’.
Todd and Kardashian’s use of these figures shows how
everyone can deploy statistical evidence to inform debate and
highlight misunderstandings of risk in people’s lives.
Judging panel member Liberty Vittert said: 'Everyone on the
panel was particularly taken by this statistic and its insight into
risk - a key concept in both statistics and everyday life. When
you consider that this figure was put into the public domain by
Kim Kardashian, it becomes even more powerful because it
shows anyone, statistician or not, can use statistics to illustrate
an important point and illuminate the bigger picture.'
1
https://www.statslife.org.uk/news/3675-statistic-of-the-year-2017-winners-announced
2
In addition to the
problems
discussed below,
the terrorist
statistics do not
include the 3000
deaths on 9/11
and also a
number of other
attacks that were
ultimately
classified as
Jihadist terrorist
attacks (for
example, the
2009 attack at
Fort Hood that
killed 14 – carried
out by a foreign-
born Jihadist –
was for several
years classified
as ‘work place
violence’).
Based on the
same time period
the number of
people killed in
the USA from
man-made
climate change is
zero. Using the
same reasoning
as in the RSS
statement one
could conclude
that climate
change risk is
infinitesimally
smaller than that
of lawnmowers,
and that
measures to
combat it are no
more rational
than President
Trump’s
measures to
combat foreign
Jihad attacks on
America
The original Kim Kardashian tweet is shown in Figure 1.
.
Figure 1 Tweet by Kim Kardashian that earned "International Statistic of the
Year" 2017
While the announcement was met with enormous enthusiasm,
one significant dissenter was Nassim Nicolas Taleb – a well-
known expert on risk and ‘randomness’. He exposed a
fundamental problem with the statistic, which he summed up in
the tweet of Figure 2.
Figure 2 Taleb's response to the RSS announcement
3
The probability of
being killed by a
lawnmower in
New York City is
especially low
because
relatively few
people there
have lawns to
mow. This
illustrates another
flaw in the RSS
risk argument – it
does not take
account of
different personal
‘profiles’: if you
do not own or
use a lawnmower
your risk of being
killed by one is
zero
Systemic risks
have long tails
that capture low
(but non-zero)
probability
events. Unlike
the lawnmower
deaths
distribution there
is a small non-
zero probability of
getting 2000
fatalities from
terrorist attacks in
a single year in
the USA.
Indeed, rather than “inform debate and highlight
misunderstandings of risk in people’s lives” as stated by the RSS,
this example does exactly the opposite. It provides a highly
misleading view of risk because it omits crucial causal information
that explains the statistics observed. These are very different for
the two different fatality numbers. One of the objectives of our
book2 is to help readers understand how to see through such
statistics and build models that incorporate the necessary causal
context.
Informally, Taleb’s argument is that there is a key difference
between risks that are systemic, which can affect more than one
person (such as a terrorist attack) and those that are not (such
as using a lawnmower) which can be considered random. The
chances that the number of people who die from a non-systemic
risk, like using a lawnmower, will double next year are extremely
unlikely. But this cannot be said about the number of people dying
from systemic risks like terrorist attacks and epidemics. The latter
can be ‘multiplicative’ whereas the former cannot. It is impossible
for a thousand people in New York City to die from using
lawnmowers next year, but it is not impossible for a thousand to
die there from terrorist attacks.
Systemic and non-systemic risks have very different ‘probability
distributions’ as shown in Figure 3.
Figure 3 Comparing the probability distributions of number of fatalities per year
2
Fenton, N.E. and M. Neil, Risk Assessment and Decision Analysis with Bayesian Networks. CRC Press, ISBN:
9781439809105 , ISBN 10: 1439809100, 2012. New Second Edition 2018
4
In the lawnmower
case Fred and
Jane are killed by
different
lawnmowers.
This is what
makes them
independent…in
absence of
common
lawnmower
design flaws
(such as a
controller bug
inserted by a
terrorist
designer).
Using the number of deaths per year to compare different types of ‘risk’
fails to consider the range of factors that affect the true risk to particular
individuals or groups. A person who does not use a lawnmower cannot
be killed by one, whereas there is a greater risk to gardeners; similarly,
residents of major cities are at greater risk from terrorists than residents
who live in the countryside. Crucially, there are also causal factors
that explain the number of terrorist deaths that need to be considered
alongside the basic statistics: terrorist cells can be responsible for
multiple deaths in a single attack, and also multiple attacks. Hence,
unlike lawnmower deaths, the deaths in terrorist attacks are related by
a common cause other than simply the artificial risk classification
(lawnmower or terrorist attack). Moreover, because as Taleb says ‘your
lawnmower is not trying to kill you’, there are extreme security
measures in place to stop terrorist attacks. If these were removed the
number of deaths would drastically increase.
Figure 4 Causal view of lawnmower versus terrorist attack deaths
These types of causal influences and relations (summarised in Figure
4) are the focus of much of our book (new edition out in Sept 2018):
Fenton, N.E. and M. Neil, Risk Assessment and Decision
Analysis with Bayesian Networks. CRC Press, ISBN:
9781439809105 , ISBN 10: 1439809100, 2012
www.bayesianrisk.com
We acknowledge the financial support by the European Research Council (ERC)
under research project, ERC-2013-AdG339182-BAYES_KNOWLEDGE. See project
website: http://bayes-knowledge.com/
http://dx.doi.org/10.13140/RG.2.2.34461.00486/1