As often happens at my place of employment, discussion devolves into a multivocal rant decrying the inability of most people to perceive relative risk. It is not just risk, either. Anything that could be considered economic in nature is absolutely a foreign language to even many mathematically sophisticated people.
Unfortunately, the human brain is terrible at modeling statistics. Part of the reason is that it has evolved to develop its own models for making estimates based on experience. The mass media have given us the ability to observe things that are far from our own experiences. Yet the quasi-experiential information received via the outlets of yellow journalism is absorbed as if actual experience. Here are some examples of things we do not consider at an appropriate level:
The National Incidence Studies of Missing, Abducted, Runaway, and Thrownaway Children study published by the Department of Justice in October 2002 gives an interesting statistic:
During the study year, there were an estimated 115 stereotypical kidnappings, defined as abductions perpetrated by a stranger or slight acquaintance and involving a child who was transported 50 or more miles, detained overnight, held for ransom or with the intent to keep the child permanently, or killed.
The number is from 1999 specifically. But forgetting about absolute accuracy, it is reasonable to estimate an incidence of approximately 1 per 2,500,000 people.
According to a Minnpost article from December 17th, 2012:
To begin with, having a gun in the home is a risk factor for serious accidental injury and death. As Hemenway points out, death certificate data indicate that 680 Americans were killed accidentally with guns each year between 2003 and 2007.
An average of 46 Americans committed suicide with guns each day between 2003 and 2007. In fact, more Americans killed themselves with guns during those years than with all other methods combined.
One study found, reports [Harvard Injury Control Research Center director David] Hemenway, that “in states with more guns, there were more suicides (because there were more firearm suicides), even after controlling for the percentage of the state’s population with serious mental illness, alcohol dependence or abuse, illicit substance dependence or abuse, and the percentage unemployed, living below the poverty level, and in urban areas.”
Two-thirds of all murders between 2003 and 2007 involved guns. The average number of Americans shot and killed daily during those years was 33.
From these data, we can say about 30,000 per year. For a population of 300,000,000, this reflects an incidence of approximately 1 per 10,000 people.
A Gannet News Service article from March 26th, 2008 claims that in 2006, 4,810 motorcylists were killed in accidents. (This is approximately 1 motorcyclists were killed for every 1,400 motorcycles registered.)
Again assuming a population of 300,000,000, this reflects an incidence of approximately 1 per 62,000 people.
So one is rather common among a small sample group (motorcyclists killed as a fraction of number of riders), but fairly uncommon for the population as a whole. A second is more common among the population as a whole. Of the three dangers mentioned, under the influence of sensationalist media, the most feared is a vastly rarer occurrence than either of the other two. That is dangerous.