A wonderful piece in the Wall Street Journal here called “The Logic of Our Fear of Flying” does a great job explaining our irrational fear of flying using concepts from math. We all know that our chances of dying in a plane crash are much lower than dying in a car accident, and yet many of us get highly stressed when our plane takes off but think nothing of getting into the car and driving at 60 miles an hour on a crowded freeway. Why?
Mathematician Eugenia Cheng explains this irrationality in three ways.
- Conditional probability. Our chances of being in a plane crash are low, but our chances of dying IF we are in a plane crash are high. If our car has an accident it could be a fender bender from which we emerge unharmed thanks to seatbelts and airbags.
- Expected values. If you may win a $300 million lottery but there are 300 million tickets sold, your expected value is $1. If you attribute the value of your life as infinity or close to it, loss of that life (despite low chances of it happening aboard your aircraft) still looks like a nearly infinite potential loss.
- Rate of change. On a plane you go from feeling very safe (on the ground) to very unsafe (during takeoff, one of two most dangerous times to be on a plane) in the space of a few seconds. The faster the rate of change of the chance of disaster, the more anxious Cheng becomes.
I read this article and thought about another risk assessment problem I talk about when I speak to lawyers and lenders around the country about my book, The Art of Fact Investigation.
It’s the paradox that companies are happy to risk handing millions of dollars a year to a relatively unknown new hire who will run a part of their business worth hundreds of millions of dollars, and that they do this while insisting that to spend more than $2,000 on a background check of that person is too expensive.
Why do people take a chance (that they will lose their company millions) when for a thousand or two they could reduce the chances of disaster?
- Conditional probability. As with car accidents, there is low conditional probability that an employee who doesn’t work out is so awful that he takes down the entire company. Hiring an MBA to run your company is not the same thing as hiring a convicted murderer on probation to do any kind of job.
- Expected values. If you characterize the downside of a bad hire as a “bad fit” at the job that can be remedied, then you as the hiring decision-maker won’t get as much blame as if you had hired the next Nick Leeson who ruins you and everyone you work with.
- Rate of change. When an employee officially “doesn’t work out” it’s usually not a surprise event but a combination of factors that have built over time. Perhaps there has been high turnover of people under that person or a string of underperforming quarters, until the company decides that person doesn’t work. The Nick Leeson rate of change (from hero to zero overnight) is rare.
In mathematical terms, then, skimping on due diligence is explainable.
Still, imagine that for some reason the air crash statistics of individual airlines were not easily available, but for $2,000 every three years you could subscribe to a service that would tell you that Aeroflot crashes a lot more per mile travelled than Qantas.
Flying on Aeroflot is still safer than driving on July 4, but many of us would probably renew our subscriptions.
Any traveler challenged on paying this kind of money for such information would tell you, “I’m just doing my due diligence.”