Innumeracy and public risk

[Note: A condensed and revised version of this article was published here in The Conversation, an online forum of academic research headquartered in Melbourne, Australia.]

Assessing risk is something everyone must do every day.  Yet few are very good at it, and  there are significant consequences to the public’s collective inability to accurately assess risk.

As a first and very important example, most people presume, as an indisputable fact, that the past century has been the most violent in all history — two devastating world wars, the Holocaust, the Rawanda massacre, the September 11 attacks and more — and that we live in a highly dangerous time today.

And yet, as Canadian psychologist (now at Harvard) Steven Pinker has exhaustively documented in his new book The Better Angels of Our Nature: Why Violence Has Declined [Pinker2011b], the opposite is closer to the truth, particularly when normalized by population [Pinker2011a]:

Believe it or not — and I know most people do not — violence has been in decline over long stretches of time, and we may be living in the most peaceful time in our species’ existence. The decline of violence, to be sure, has not been steady; it has not brought violence down to zero (to put it mildly); and it is not guaranteed to continue. But I hope to convince you that it’s a persistent historical development, visible on scales from millennia to years, from the waging of wars and perpetration of genocides to the spanking of children and the treatment of animals.

How could the public perception be so wrong? The news media is partly to blame — good news doesn’t sell much advertising space. But the problem might go even deeper: We may be psychologically disposed to miscalculate risk, perhaps as an evolutionary response to danger. One well-known problem is the “conjunction fallacy” — the common predilection to assign greater probability to a more specialized risk.

For example, Pinker recently presented five scenarios for worldwide calamity on a website and then asked respondents to rate each according to risk. Two of the five were (2): A nuclear weapon will be set off in a war or act of terrorism; and (4) Iran will provide nuclear weapons to a terrorist group that will use one of them against Israel or the United States. Roughly half of the subjects assigned the second scenario more likely than the first, even though the conjunction of two events clearly has lower probability than either event by itself [Pinker2011b, pg. 369].

One indication of our inability to objectively assess risk is the fanatical and often counter-productive measures taken by parents nowadays to protect children. For example, 42 years years ago 67% of U.S. children walked or biked to school, but today only 10% do, in part stemming from a handful of highly publicized abduction incidents. Yet the number of cases of true child abduction by strangers (as opposed to, say, a divorced parent) has dwindled from 200-300 per year in the 1990s to only about 100 in the U.S. today. Even if one assumes that all of these children are harmed (which is not true), this is still only about 1/20 the risk of drowning and 1/40 of the risk of a fatal car accident [Pinker2011b, pg. 444].

Such considerations many not diminish the tragedy of an individual loss, but they do raise questions of priority in prevention. For example, governments worldwide often agonize over marginal levels of additives in certain products (agar in apples in the 1980s and asbestos insulation in well-protected ceilings), while refusing to spend money or legislate for clear social good (smoking in the developing world, gun control, infectious disease control,  needle exchange programs and working conditions in coal mines).

One completely absurd example is the recent surge of opposition in the U.S. (supposedly on health concerns) to “smart meters,” which once an hour send usage statistics to the local electric or natural gas utility [Barringer2011]. Yet the microwave exposure for these meters, even if one is standing just two feet from a smart meter when it broadcasts its data, is 550 times less than standing in front of an active microwave oven, up to 4600 times less than holding a walkie-talkie at your ear, and up to 1100 times less than holding an active cell phone at your ear. It is even less than sitting in a WiFi cyber cafe using a laptop computer [SDGE website].

A much more serious example is the ongoing hysteria, especially in the U.K. and the U.S., over childhood vaccinations. Back in 1998, a study was published in the British medical journal Lancet claiming that vaccination shots with a certain mercury compound may be linked to autism, but other studies showed no such link. But in the meantime, many jumped on the anti-vaccination bandwagon, and several childhood diseases began to re-appear, including measles in England and Wales, and whooping cough in California.  We should note that the rate of autism is probably  increasing (see Conversation article).

Finally, in January 2011, Lancet formally acknowledged that the original study was not only bad science (which had been recognized for years), but further an “elaborate fraud” [NYT2011]. Yet nearly one year later, opposition to vaccination remains strong, and irresponsible politicians such as would-be-US-President Michele Bachmann cynically (or ignorantly?) milk it.

A related example is the worldwide reaction to the Fukushima reactor accident. This was truly a horrible incident, and we do not wish to detract from environmental devastation that occurred [Tabuchi2011]. But we question decisions such as that quickly made by Germany to discontinue and dismantle its nuclear program. Was this decision made after a sober calculation of relative risk, or simply from populist political pressure? We note that this decision inevitably will mean more consumption of fossil fuels, as well as the importation of electricity from France, which is 80% nuclear. Is this a step forward, or a step backward? We note that concern about global warming is, if anything, more acute than ever in light of accelerating carbon consumption [Gillis2011].

[Added on 17 Mar 2012 and 18 Jul 2012: The latest analysis indicates that the initial concerns of health effects from nuclear leaks at Fukushima are overblown, and that Fukushima, in any event, is not at all in the same class as the Chernobyl incident — see New Scientist article #1 and New Scientist article #2.]

[Added on 17 Mar 2012: As another example, recent concerns that cell phone usage by pregnant mothers endangers their fetuses are wildly exaggerated — see New Scientist article #3.]

This kind of over-reaction — to which many of us are prey — is exacerbated by cynical and exploitive individuals, such as Bill and Michelle Deagle and Jeff Rense, who profit from such fears by peddling bogus medical products, speaking at conspiracy conventions for hefty fees, and charging for elite information. This is just one instance of a large growing and dangerous co-evolution of creationist, climate-denial and other anti-science movements — see Math Drudge blog and Ecker2011.

How do we protect against such misinformation and misperceptions? The complete answers are complex but several things are clear. First of all, science education must be augmented to address the assessment of risk — this should be a standard part of high school mathematics as should be more attention to the information needed to make informed assessment (see Conversation article).  Secondly, the press needs to be significantly more vigilant in critically commenting on dubious claims of public risk — citing literature, consulting real experts, etc. Ideally, we should anticipate scientifically trained and certified scientific journalists. Thirdly, mathematicians and scientists themselves need to recognize their responsibility in helping the public to understand risk. Failure to do so, well, poses a serious risk to society.


  1. [Barringer2011] Felicity Barringer, “New Electricity Meters Stir Fears,” New York Times, 30 Jan 2011, available at Online article.
  2. [Ecker2011] Ulrich Ecker and Stephan Lewandowski, “Why The Guardian’s correction won’t change your mind about Milly Dowler,” The Conversation, 17 Dec 2011, available at Online article.
  3. [Gillis2011] Justin Gillis, “Record Jump in Carbon Emissions in 2010, Study Finds,” New York Times, 4 Dec 2011, available at Online article.
  4. [NYT2011] [Editorial], “Autism Fraud,” New York Times, 12 Jan 2011, available at Online article.
  5. [Pinker2011a] Steven Pinker, “A History of Violence: Edge Master Class 2011,” 27 Sep 2011, available at Online article.
  6. [Pinker2011b] Steven Pinker, The Better Angels of Our Nature: Why Violence Has Declined, Viking, New York, 2011.
  7. [Tabuchi2011] Hiroko Tabuchi and Martin Fackler, “More Radioactive Water Leaks at Japanese Plant,” New York Times, 4 Dec 2011, available at [Tabuchi2011].

[A version of this article appeared in The Conversation.]

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