A Rational Shark-Bite Victim — and She's Only 10

In SuperFreakonomics, we write about shark attacks as anomalous events that tend to make a lot of noise and therefore persuade many people that they aren’t such anomalies.

A reader named Michael McDonald sends along encouraging evidence that at least one person is thinking clearly on the matter. A young girl named Caitlin Dubois gets nibbled on by a shark in New Smyrna Beach, Fla., and won’t even consider staying out of the water:

“I like swimming in the ocean,” she said. “It’s a freak thing, and a one-in-a-million chance that I would get bitten by a shark. So it really wouldn’t happen again, I don’t think.”

Here’s what Michael wrote:

Could not help but read [this] and smile that this 10-year-old girl grasps the irrationality of being afraid of something that 1) has overwhelmingly long odds of ever happening to us (shark bite); and 2) has already happened to her. Somehow this little girl understands what so many adults in a similar situation would walk away with the opposite conclusion (the mental certainty that they are somehow “prone” or at least very likely to experience another bite). Maybe our next generation isn’t as troubling as our bias leads us to believe….or, more likely, this girl is untainted as of yet by adults’ fear-mongering.

Surely we don’t know enough about her yet to start a Caitlin-for-President movement, but still, it is tempting.


Shay Guy

I wouldn't be surprised if she were scared anyway, though, even if she knows it's irrational.

Nosybear

I admire her courage but there's still an error in her reasoning. She seems to think because the rare event has already happened to her, there is no chance of it happening again when the probability really is exactly the same as it was before she was bitten. Still, she shows a bit more of a grasp of the reality of the situation than most adults. As far as Caitlin for President, I don't know but if she were in the Colorado Senatorial race (or even, maybe Gubernatorial), she'd have my vote, far superior to the current pack in reasoning skills and lack of bias.

Rudiger in Jersey

If Caitlin--God Forbid-- was eaten and killed by a shark, she would not give the same smarty comment.

You are looking at a survivors bias. Talk instead to the parapalegic whose life is permanently altered and is unable to swim because they are missing legs and arms.

Brian

This is a great story, and thanks to Michael for pointing it out. I couldn't help but notice, however, that Michael seems to be suffering from a bit of irrationality himself. If successive shark bites are independent random events (which I assume they are), it doesn't make any sense to add "and 2) has already happened to her." Having already been bitten by a shark neither decreases nor increases Caitlin's odds of being bitten again, just like flipping heads 400 times in a row neither decreases nor increases my odds of flipping heads on the 401st attempt.

Brenton

Rudiger, if the situation involved a car accident rather than a shark attack, would you be saying the same thing? I really don't understand how her reasoning has anything to do with a survivorship bias. Maybe it would be a survivorship bias if she was saying something like "when I get bit again, I'll probably live, since I survived the last attack".

Tumbolian

I think the point behind (2) is that those to whom a highly-improbable event has occurred would typically overestimate its likelihood, whereas Caitlin has managed to avoid such a biased adjustment to her estimate of the probability.

Edward S

It's not clear from her comment that she is using the gambler's fallacy (that because it happened it's less likely to happen again). The base rate of shark attacks is so low that her comment could simply mean the chances have returned to the base rate (rather than actually being lower post-shark attack). The difference between the base rate and zero is quite small so it would be hard to distinguish the two beliefs based on casual language ("it really wouldn't happen again, I don't think").

Her comment is impressive in either case because she's resisting the human tendency to assign too much meaning to personal experiences (especially very memorable, emotional experiences like shark attacks) in predicting future events.

Mike

Brian -

I think Michael would have been much better served by saying, "... yet 2) ..." instead of "... and 2) ..." I like to think that's what he meant.

Eric M. Jones

Then again, perhaps her body possesses the eleven secret herbs and spices particularly yummy to sharks.

You've got to wonder when someone has either good or bad fortune on a continuing basis...

Samy

Brian, in Michael's defense, he did say "...the irrationality of being afraid of something that 2) has already happen to her." I don't think this reads as "it's irrational to not think that your odds of being bit by a shark are less after you've been bit already once," but instead reads as "it's irrational to think that your odds of being bit by a shark are greater after you've been bit already once." He's talking about the the "mental certainty" of being "prone" to a second bite as being irrational, not some change in the odds.

Surely, lots of people have post-traumatic irrationalities about getting in a car or swimming in the open ocean. Some people just have a fear of sharks, it's very primal. They effectively represent the ultimate predator. I've never been bit even once, and I never plan on snorkeling.

David B

"If successive shark bites are independent random events (which I assume they are), it doesn't make any sense to add 'and 2) has already happened to her.'"

I had to read this several times, most of the way mounting the same objection you mount. However, if we give Michael the benefit of the doubt, it is possible to interpret paragraph as saying "1) and 2) usually combine in an irrational way (that is, people assume they are MORE likely to be attacked again), but that type of thinking is resisted here."

I'm all for fighting against the Gambler's Fallacy as often as possible, but let's make sure that we don't assume that an overall intelligent observation is suspect just because it's a little difficult to interpret.

Jared

Uh oh... what if the error term is correlated with the independent variable?! Like, what if her flesh tastes particularly good to sharks?! Dear lord. Someone phone Caitlin and explain endogeneity to her quickly!

CaptainOblivious

I read the "not being afraid of something that's already happened" part as simply not fretting over the past. Like when you're nearly in a car wreck, and you get all worked up about "what if I hadn't hit the brakes fast enough" or whatever. There's really no need to "worry" about such a thing, because it's in the past - you DID hit the brakes fast enough.

Similarly, there's no need to cringe when you see a big blast of lightening - the fact that you're still alive proves that it didn't actually kill you, and the thunder is relatively harmless.

Clancy

I don't think Michael or Caitlin was claiming that being bitten once reduced her chances of being bitten again. Caitlin was saying that the probability is unchanged--still one-in-a-million--which is close enough to zero to ignore.
Michael was just saying that being bitten would cause most people to be (irrationally) more afraid of it happening again.

I'd be interested to know if Caitlin's mother's reaction was quite as rational.

Rudiger in Jersey

#5 Brenton,
You can only interview the SURVIVORS.
The DEAD do NOT SPEAK.
But they may have an stong opinion on the matter too.

Therefore interview near death victims as well as the ones who got a papercut.

Lulu

The attacks aren't randon here. We live in the city with the most shark bites in the entire world. People get biten by sharks every weekend.
http://en.wikipedia.org/wiki/New_Smyrna_Beach,_Florida#Shark_Attacks

Rudiger in Jersey

Apparently Caitlin was too young to have seen the Premiere of the Movie Jaws.
Ocean swimming dropped of dramatically for years.

These kids by comparisons are palpably afraid of every strange adult as a likely candy distributing perverted rapist kidnapper when this likelihood is also as rare as man-eating sharks.

AaronS

Listen, every time I get in the water, every shark between here and Key West stops what they are doing, magically alerted to my presence, and says, "HEY!!! Aaron's in the water!"

Why haven't I been bitten. Well, first, only a very large shark could take me...and I don't get deeper than knee-deep (in order to see their huge fin sticking out of the water as they approach to kill me).

Second, I talk my wife into going somewhere else.

Lastly, I laugh when people tell me how ONLY, say, 60 people were killed all last year of all the millions of people in the water. To which I respond, "Yeah? How many had their legs chewed off? their hand removed? their pants soiled? and their psyche ruined forever?"

If every shark were dead tomorrow, I would be as sad as if every rattlesnake were dead tomorrow. They've had the beach for millions of years--IT'S MY TURN NOW!!! (at least when they're all gone, it will be).

Read more...

Ray

Well, the validity of this argument is predicated on the fact that Caitlin's preferences for swimming (and presumably risk) have not changed. If Caitlin came out and said that she did not like swimming anymore or that she is much more risk averse now, then it would be rational for her not to go swimming anymore.

Of course, you can argue that no one should change their tolerance for risk or preferences for swimming after a traumatic incident but this would be very difficult to implement and, frankly, understand.

Sarah

Ok, maybe this has already been said, but it doesn't seem to me she is implying that she's less likely to be bitten because she already has been. She's just saying it's not a very likely event so it's still unlikely that she'll be bitten in the future. Just like it's unlikely for any other individual to be bitten in the future.