Bryan Caplan  

The "Zero-Probability Fallacy" Fallacy

Why the U.S. is Ungovernable... Clemens on Haiti...
Lenore Skenazy's Free-Range Kids has 58 5-star reviews on Amazon - and only one 1-star review.  But Olga, the book's lone detractor, makes a striking argument: The real innumerates are not paranoid parents, but people like me and Skenazy who mock them.
According to Lenore, if the chance of your child being abducted and tortured to death by a stranger is only 1 in 610,000, then you should simply act as if the real number is zero. Using this type of logic, I should discontinue wearing my seatbelt every time I get in the car. It's uncool. Paranoid. The chance of dying in a car accident is only 1 in 100 over my lifetime, so, it might as well be nothing...

Well, 115 children in the US are abducted by strangers, sexually assualted and murdered every year. 115 yearly. That isn't an urban myth. It isn't a horror film. It isn't a Stephen King novel. It's 4 classrooms full of children.

There is a difference between "rare" and "non-existent". In the face of any kind of preventable risk, a parent has a responsibility to work to prevent the event, regardless of the odds against it ever happening.
My reply to Olga: Yes, there is a difference between "rare" and "non-existent."  Taking precautions against a non-existent danger is silly; taking precautions against a rare danger might be wise.  So far, we agree.  My objection: All parents, including you, frequently fail to try to prevent risks.  Why?  Because after you reduce a risk - for example, by buckling your child's seat-belt, a risk still remains.  Buckled children still get injured.  And that risk is also preventable!  You could make your child wear a helmet in the car to further reduce the risk of head injury.  You could make him wear thick clothing - or a face mask - to protect him from shattering glass.

Or you could just stay home, brick up your windows, and make your kid wear a bullet-proof vest.

I bet even Olga would admit that these precautions are absurd.  But what makes them so?  Simple: They only slightly increase safety at a large cost.  Which is precisely Skenazy's objection to Today's Typical Parents' effort to prevent child abduction.  She doesn't advocate zero precautions.  She explicitly tells her kids not to "go off with strangers."  But she uses probabilities to convince readers that the additional precautions parents take - like keeping nine-year-olds under continuous observation - are absurd.

Of course, parents' risk-aversion varies.  But it's still fair to ask them do comparative risk analysis.  If you're willing to drive your kids to the mall, and car travel is forty times more lethal per minute at unsupervised mall loitering, then why will you allow the former but not the latter?

Olga ends with a challenge to Skenazy: "Who are you to claim that the antidote to 'unrealistic fear' is to dishonestly give your children a false sense of security?"  But this just raises a deeper question: What is a "true sense of security"?  If it requires absolute safety, then no one could ever justifiably feel secure.  That's ridiculous.  If you can't feel secure - and teach your children to feel secure - about 1-in-610,000 nightmare scenarios - the problem isn't the world.  It's you.

Comments and Sharing

COMMENTS (21 to date)
Rich writes:

Does the book in question discuss selection bias? Is it possible that the number would not be 115, but rather a much higher number, if every parent acted as though 1/610,000 = 0?

Matt writes:

Maybe in Selfish Reasons to Have More Kids you should give us an equation for when to apply a safety precaution based on how much it improves the odds of survival against the cost. The cost of applying the safety standards could also be weighed against the costs of losing a child (loss of tax break for dependents, looking like an irresponsible person, emotional trauma...) You could be as cool as these guys.

Dave writes:

Bryan, Since parents so grossly overestimate the risk of their kids being murdered, you could make a fortute underwriting kid-murder insurance policies.

Steve Horwitz writes:

All right on Bryan. I'd add one other point:

It's not just comparative risk, it's also cost-benefit analysis. It's true that free-ranging your kids adds a fractional amount of risk to their lives, but it also brings significant benefits by encouraging their independence and self-reliance. It also, as you have rightly pointed out many times, makes YOUR life easier as a parent and enables YOU to get things done while your kids amuse themselves.

I have friends who constantly complain about how they can't get anything done when they are home with their kids. I suspect that they feel compelled to monitor/play with the kids every freakin' moment, so no wonder they can't do work or even clean the house.

Some risks are simply worth taking when they are low enough.

Outlawyr writes:

Maybe I'm missing something (and I haven't read the book), but one probable reason abductions are relatively rare is that so many people take precautions. We have a guarded kids norm. Most people pitch in. Parents often watch out for other stray kids and step in to help when guards are down. So do security guards, store managers and neighbors. If we all quit our vigilance, maybe abductions would go way up. Sure, some people like the author, free ride on our collective norm and maybe such cheating is rational (public goods problem?), but I think the status quo works. So, maybe those precautions look cost-unjustified they've worked.

Outlawyr writes:

In other words - see Rich's post.
People who let their kids roam free are tsk tsked and chattered about because we need to shame them into maintaining the norm and holding up their end of the burden, otherwise cheating would become rampant and our kids would be in greater danger.

Dan Weber writes:

It's true that abduction rates might be higher if we relax our sphincters for a minute.

But when you are dealing with less-than-1-in-10,000 probability risks, a little unclenching won't hurt. Worry more about the real risks your kids face.

Tuttle writes:

"We have a guarded kids norm. Most people pitch in. Parents often watch out for other stray kids and step in to help when guards are down. So do security guards, store managers and neighbors. If we all quit our vigilance, maybe abductions would go way up."

Straw man - the position which you ascribe to Bryan is not held by him. Neither the author nor Bryan proposes quitting our vigilance or letting out guards down.

Rather, they recommend taking "reasonable risks." And what makes these risks reasonable? Well, precisely the vigilance which you describe in detail.

It is only because normal people look out for each other, only because we live in an extremely safe society, that Bryan and the author consider "free ranging" to be a reasonable risk.

dullgeek writes:

This reminds me of what I've heard Mike Munger say about economists, "an economist is someone who believes, sincerely believes as a matter of moral justice, that the infant mortality rate should be positive".

Clearly, Olga is not an economist.

Tuttle writes:


I agree, but you're a bit off on the 1-10,000 risk rate. Child abduction-murder is closer to around 1-1,000,000, iirc.

MikeP writes:

Dan is talking about "less-than-1-in-10,000 probability risks".

The average American has a 1-in-10,000 chance of dying in a car accident each year. Yet few if any of us think twice about that before getting in a car.

Dan's point is that you should think twice about thinking twice about something one or two orders of magnitude less likely than dying in a car accident.

Yancey Ward writes:

And thus begins the child car-helmet/face guard movement.

Tom West writes:

The woman's response pretty much summarizes my explanation (in the previous article) for the current behaviour.

One point, however, that seems to be missing is that all of the child safety measures that society demands of parents are assumed to be free of cost. There's no penalty for taking your children on a drive, because the cost of not driving your children is way higher than the benefit.

However, the cost of *not* giving them freedom is assumed to be zero. Therefore if you do and something bad happens, you might as well have been harming the child yourself as far as society, your peers, and your family is concerned. Certainly the way I was raised (not a huge amount of freedom, but taking 15-mile bicycle expeditions in the city by age 10) would probably rate criminal charges nowadays (if something bad happened).

In other words, don't be too hard on the parents - you have to be willing to flirt with near criminality to *not* overprotect your children. (I'm still all tense every time I send my 10 year-old alone to the grocery store three blocks away until he returns.)

Loof writes:

In Thailand, economists statistically proved there was a far greater risk to get injured as a motorbike driver than children as passengers. So, balancing costs with benefits drivers are legally required to wear helmuts; children are not.

Libertarian economics can indeed tell us something about risk aversion extremes and reasonable risks in the example of giving a child free range in the car when driven to the mall for a free range to loiter. Loof also supposes that when bored with loitering the pampered child might be driven to school to hang out in the hall or driven back home to dawdle about.

Paranoid parents see too many problems that really aren’t – and, pampering parents, at the other extreme, are blind to problems that really are. Both types of parents negatively treat their children with excessive attention. In looking at problems: paranoia puts the problem in too many frames; pamperers know not how to frame the problem.

Tom West writes:

Paranoid parents see too many problems that really aren’t – and, pampering parents, at the other extreme, are blind to problems that really are.

To reiterate my thesis, if you are facing social, familial, and possibly legal opprobrium for not over-protecting your child, it's not paranoia, it's deferring to (unfortunate) social norms.

In a middle-class urban environment, free-ranging your children is considered one step above drunk-driving - i.e. you're putting the innocent at risk for your own selfish reasons.

Loof writes:

Tom’s thesis is a basketcase for collective paranoia if it’s a social norm; and perhaps part of a case of Americans’ becoming increasingly fearful overall.

jb writes:

Concrete benefits, diffuse costs.

Simplistic Analysis:

The concrete benefit - you feel more certain your child is safe. The diffuse cost - your child may not develop and grow as much as they might if you gave them more freedom.

But the *may* in that statement is so diffuse that most people discount it to zero. And the chance of losing a child to abduction is (slightly) > 0

More sophisticated analysis
Consider the consequences of future results: if my kid is abducted, I will think about all the things that I should have done to keep them safe. If I make any mistakes, relax my vigilance at a time when the child is abducted, I will never forgive myself, and ruin the rest of my life with my self-loathing. Plus, all my neighbors and family will blame me (rightly) for allowing this to happen.

In that scenario, while the risk of abduction is still quite low, the personal cost is astronomical. Multiply the two together, and you still have a cost to you > benefit to the child

Even more sophisticated analysis:

While it is true that I will blame myself if my child is abducted, the fact is, I will blame myself no matter what, even if I was a diligent, attentive, hovering, smothering parent. So the costs will be huge either way - realistically, they are sunk costs, inherent in the nature of being a parent who loves his or her children.

And, of course, we should treat sunk costs as 0.

In that scenario, and only in that scenario, do the benefits outweigh the costs.


To the other point - it would appear that some people think abductions are down because of the helicopter hovering smothering parents. In this case, helicopter hovering smothering parents are a vaccine to the disease of abduction. Therefore, a public good. Herd immunity will be weakened by a few parents defecting from the Hovering Smothering vaccine, and, potentially, raising the risk of contracting the abduction disease across the entire herd.

This presumes, of course, that there are lots of sexual predators/murderers out there, who are lurking about, waiting for the chance to abduct a child, perpetually stymied by the Hovering Smothering vaccine. I find this presumption hard to swallow. There are still plenty of children who amuse themselves unsupervised - these are typically called 'poor kids'. But yet the stereotypical stranger abductions are still miniscule.

It seems to me there are two things that we can do that manage the risk, instead of letting it manage us:

1) Give your kid a limited-access cellphone
2) Give them a lot of freedom unless there's a stereotypical stranger child-abduction in your area. Then, take additional precautions.

mattmc writes:

"I bet even Olga would admit that these precautions are absurd."

Maybe, but I think there is a huge case to be made for rethinking auto safety. Wearing a helmet certainly seems like a reasonable accommodation for possible head injuries. What I don't understand is why we aren't driving bumper cars around. We have the technology to build vastly more cushioned systems than we have today. I would gladly buy a car that is more egg carton than Ferrari. I barely have chance to drive fast anyway. Are we really sacrificing so many lives to fashionable looking cars? I would pay twice as much for a car that cut my death risk in half.

Kurbla writes:

Again, there is not enough analysis for the conclusion you try to reach. If life of one's kid is worth $1 billion for his parent; if solving life treating problem with probability of 1/million has price of $500, then it could be actually reasonable decision.

More numbers, less words.

jean writes:

There are other possibilities:
_If parents let their kids wandering, the probability of an assault might raise dramatically. Assume that only 1 out of 10000 kids are let wandering and that only these kids have trouble, then the probabilty raises to one over 61, which much higher.
(My point is that you shouldn't look the rate of abduction but the rate of abductions among non-protected children, which is probably much higher.)
_Second, abduction is not the only danger the kids are exposed out. They might be in contact with drug traffickers, money racketteers...

marie Bargo writes:

Possibly you can assist me! I am looking to buy a motorcycle for my boy and i simpy dont know what i should be going for? I mean when i got my motorcycle i knew exactly what i wanted for a ver long time, but he is unsure what he wants? Is there maybe a good way to determine whats best?

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