The Multiple Endpoints Phenomenon

If you haven't yet read it, I highly recommend Thomas Gilovich's How we know what isn't so: The fallibility of human reason in everyday life. It's a very good and entertaining (to an infophiliac, at least) read, covering a lot of the reasons that people end up believing many stupid things. Most of the concepts he discusses in it are now in common use in the Skeptical community, such as the confirmation bias, pareidolia, the Texas sharpshooter fallacy, and others.

But there's one big one that seems to be missing, for some reason: The multiple endpoints phenomenon. The discussions surrounding shoehorning come close to it, but I feel that this is a subject that deserves consideration and study on it's own.

So what is it?

Avid watchers of Everybody Loves Raymond may remember this scene. Ray and his brother, Robert, are having a little competition over who can be the first to toss a kernel of popcorn (or something, let's say popcorn) into a bowl. They alternate tosses for a while, both of them consistently failing. Eventually, Robert grabs a double handful of popcorn and tosses it at the bowl. A few fall in, and he immediately claims victory.

Breaking it down, here's what happens: At first, they try to throw the popcorn in individually. This has a single endpoint of success: that the popcorn goes in. Then Robert throws a bunch at once. This has multiple successful endpoints: one for each individual kernel going in. A few of these go in, so Robert claims success. He points to the endpoints he reached and used those declare victory.

Simply put, the multiple endpoints phenomenon describes how if you have a specific measure for success, it's hard to achieve it, but the more you generalize it, the easier it gets. What you have to watch out for is people who act like they had a specific measure when in fact they were going from more generalized criteria.

For another example, try to find someone who shares your birthday. Not very easy, as only one out of every 365 people will (discounting leap years here). Now, try to find any two people who share the same birthday. Chances are you'll find a pair before you've asked even 30 people. Making your search just the tiniest bit more vague in this case makes it take 1/12 as long, as you have many more places you can end up. (Okay, my math might be off slightly, but I don't have a decent calculator with me right now.)

And now, here's the trick. Turn it around, and ask what the odds are of this occuring in a vacuum. What is the probability that these two people would share a birthday? 1/365. What you're doing now is pretending that this particular endpoint is what you were shooting for, rather than just one of many possibilities, making it look like something special has happened here.

Where do we see this happening?

The multiple endpoints phenomenon shows up in many places, but I've chosen just three to highlight here which I believe will have relevance to my audience. You've probably seen these before, but understanding of multiple endpoints will help illuminate the patterns and allow you to spot similar circumstances in the future.

1. Cold Reading

John Edwards: I'm getting something... possible an "A" or an "M"...

Woman in audience: My husband Adam just died! *sob*

John Edwards: Yes, that's it!

*Audience applauds*

Step 1: John Edwards makes a generalized prediction: someone in the audience will be there with something in mind that has an "A" or an "M." He's setting up many, many endpoints.

Step 2: One of the endpoints is a hit. The woman's husband, Adam, just died, and "Adam" has 2 A's and an M. Quite fitting, but in an audience that size, very likely that someone would say something.

Step 3: Edwards claims that this was what he was sensing in the first place. He's gone back and changed his original prediction from one with many endpoints to one with just a single endpoint to make it look like something amazing has happened here.

Step 4: John Edwards is nominated for and wins the title of "Biggest Douche in the Universe."

2. Pseudoscience

Fred Sicher and Elisabeth Targ set up an "experiment" to determine if prayer (or directing "positive energies" at a person) would improve their health. In this particular study, they set up a decent, randomized, double-blind test with twenty AIDS patients received Distant Healing (or DH) and twenty being a control group. The study set out to test the death rate of the patients.

At the end of the study, only a single subject had died. This meant that the results were inconclusive, or that they failed to confirm the hypothesis the DH has an effect. If they'd stopped there, it would have been good (if ultimately useless) science. But in the end, they twisted it to make it look like DH actually worked.

What happened is that after this result, Targ urged the researchers to change the goal of the study to instead measure the effect of DH against a long list of AIDS-related symptoms. When they found that the subjects in the DH group stayed in the hospital and visited doctors significantly less than the control group, they reported on their study as if this was the original. They even failed to mention that in one category, psychological stress, the DH group was significantly worse than the control group.

Step 1: They casted the net wide, allowing for a significant change in any one of multiple criteria to count as a success for DH. Many endpoints are set up.

Step 2: A couple criteria were found in which DH had statistically significant positive results. But they were studying 23 criteria, and the threshold p-value was 0.05. Seems quite likely that at least one would fit it. They had multiple ones, but some, like number of hospital visits and days spend in the hospital, would be expected to have a high correlation. A few of these endpoints are hit.

Step 3: They report only on the criteria that yielded positive results, and acted as if this was what their study had set out to test in the first place, making it look like DH worked.

Step 4: Targ dies of a brain tumor in 2003, despite being one of the most prayed-for people on the planet.

(Source: http://skepdic.com/sichertarg.html)

3. Everyday Life

There are many coincidences that could occur in your life on any given day. You might be thinking of someone the moment they phone you. You might be thinking of a particular episode of a TV show, and it's on later that day. You might run into someone with the same name as you. You might be thinking of a person you haven't seen in a long time, and then later hear mention of them.

The possibilities are countless, and many of them do come up. Thanks to the confirmation bias, the few hits are remembered while the misses are forgotten. In this way, we fool ourselves into thinking that we started off with many fewer endpoints than we actually did, so seemingly unlikely stuff must be happening more than it should.

Every future coincidence only adds to this pile of evidence, until eventually you determine that there just has to be some force guiding the universe.

Edit: Browsing the Swift archives, it appears that there is indeed some nutjob claiming that all coincidences are winks from God proving his existence. Read about it here (Unfortunately, the original article it references is no longer available). Let's just hope not too many people fall for this.

Conclusion

Once you understand it, multiple endpoints is a potent weapon in the Skeptic's arsenal. It shows up in many more places than you might think. The problem you might face is in explaining it to others. For that, I recommend a metaphor like the ones I used earlier in this post or "It's like fishing with a net, and then, once you catch a fish, claiming you nailed it with a spear."