Beware the Rare Event

Carl Bialik, “The Numbers Guy” at The Wall Street Journal, notes that

a 1-in-5.2 million shot came through in Bulgaria, as the same six winning numbers turned up in two consecutive drawings. And 18 Bulgarians profited by betting on recent history: They chose the winning combination of numbers from the drawing four days earlier — which hadn’t been selected by anyone the first time around — and split the pot.

The coincidence drew international news coverage and sparked a probe by a government-appointed commission. Bulgarian officials ultimately chalked it up to coincidence. . . .

The general principle . . . is that this would have happened eventually. There are lotteries in dozens of countries, and multiple ones within countries — scores in the U.S. alone. Many of these lotteries have had multiple drawings each week for decades. If there have been, say, a million lottery drawings, then a coincidence as unlikely as this one becomes more of a 1-in-5 yawn. That still means that any one player’s chances of winning the lottery are close to zero.

In short, regardless of less-than-amazing coincidences, it is a rare event to hold the winning number in a lottery.

People are drawn to coincidences of the kind described by Bialik
because the coincidences are rare events, as are celebrity scandals (as opposed to the relatively stable marriages of “ordinary” people), aircraft accidents that take 200 lives (as opposed to myriad uneventful flights), the acts of murderers and other violent criminals (as opposed to the relatively civilized behavior of most people), and so on.

A problem with rare events — “outliers” in the terminology of operations research — is that, despite their rarity, they attract a disproportionate share of public and political attention. They skew our perceptions of normality. A rare but notorious tragedy usually is followed by calls for government to “do something” to prevent future tragedies of similar kinds.

Consider, for example, the National Highway Traffic Safety Administration (NHTSA), the Occupational Safety and Health Administration (OSHA), and the Consumer Product Safety Commission (CPSC). All three agencies were established in 1970-72, in the wave of fear-mongering that followed the publication of Ralph Nader’s Unsafe at Any Speed. All three agencies were inspired by the occurrence of relatively rare events. And those occurrences had been in decline long before the establishment of NHTSA, OSHA, and CPSC.

I introduce in evidence Figures 1 and 2 of “Safety at Any Price?” by W. Kip Viscusi and Ted Gary (Regulation, Fall 2002, pp. 54-63), which indicate that unintentional injury deaths in the United States had been falling steadily, long before the advent of NHTSA, OSHA, and CPSC.* In 1928, the first year treated by the authors, the annual rate of unintentional injury deaths arising from accidents of all kinds was only about 80 per 100,000 persons; that is, about 8/100 of 1 percent of the population died of unintentionally inflicted injuries.  By 1960, the rate was only about 5/100 of 1 percent of the population, and by 1990 it was down to 3.5/100 of 1 percent of the population, where it has leveled off.

In other words, the incidence of fatal accidents declined faster before the establishment of NHTSA, OSHA, and CPSC than it has since. NHTSA, OSHA, and CPSC have had no demonstrable effect on the incidence of fatal accidents. Why? Because human beings tend to act responsibly, for the sake of self-preservation. When, on rare occasions, they fail to act responsibly — or their machinery fails them — they can be counted on to learn from their misfortunes and the misfortunes of others. And there is nothing new about learning from experience and applying that learning to improve our material possessions. Just ask a caveman.

What, then, is the role of NHTSA, OSHA, and CPSC? They are like cheerleaders who claim credit for their team’s victories because they cavort on the sidelines for the entertainment of the crowd. Cheerleaders notwithstanding, the team generally does what it was going to do, anyway, except when a cheerleader gets too close to the action and obstructs it. Sometimes a cheerleader’s obstruction accidentally benefits the cheerleader’s team; other times, it hurts the cheerleader’s team. There are three main differences between NHTSA, OSHA, and CPSC and cheerleaders. Cheerleaders (a) aren’t supposed to interfere with the players (and rarely do); (b) they provide their services relatively cheaply or free of charge; and (c) they are more attractive than most bureaucrats.

The occurrence of a rare event should be an occasion for noting that it is a rare event. It should not be an occasion for the creation of a costly, intrusive, and essentially ineffective regulatory agency or a sheaf of misguided regulations.


* Figure 1 seems to show a general rise in the rate of deaths from motor vehicle accidents between 1945 and 1975. That increase  is explained by the growing use of automobiles. As shown in Figure 2 of the Viscusi-Gayer article, death rates per vehicle and per vehicle-mile had been dropping steadily until 1960, when those rates rose slightly for a few years before continuing to decline. For more about the long-term trend in deaths from motor-vehicle accidents, see this post, which also includes a discussion of the Peltzman effect: “the hypothesized tendency of people to react to a safety regulation by increasing other risky behavior, offsetting some or all of the benefit of the regulation.” There is more evidence for the Peltzman effect in this article.