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.
and 
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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…
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.
“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.
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!
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.
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.
#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.
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