The children adjusted their hypotheses appropriately when they saw the statistical data, just like good Bayesians—they were now more likely to wave the block over the toy, and you could precisely predict how often they did so. What’s more, even though both blocks made the machine light up twice, the 4-year-olds, only just learning to add, could unconsciously calculate that two out of three is more probable than two out of six. (In a current study, my colleagues and I have found that even 24-month-olds can do the same).
There are other examples of kids thinking like Nate. All polls depend on the idea of sampling. If you poll a relatively small number of voters in a truly random way, then you can figure out the choices of the other voters you didn’t poll. Even 8-month-olds seem to understand something about sampling. Fei Xu at the University of California-Berkeley and her student Vashti Garcia used a “looking-time” technique, which depends on the fact that babies look longer at unexpected events. The experimenter showed the infants an opaque box, and then she closed her eyes, randomly took some colored pingpong balls from the box, and put them in a small bin. She might take out four red balls, for example, and only one white ball. Then the babies got to see inside the box. Sometimes they saw that the box mostly had red balls in it with just a few scattered white ones—that makes sense if the 4-to-1 sample was truly random. But sometimes the box didn’t match the sample—the kids might see the experimenter take mostly red balls out of a box that was mostly white. Babies consistently looked longer when the sample wasn’t random than when it was.
The unlikely events in this experiment weren’t impossible—you could, after all, pull mostly red balls from a mostly white box. But they were very improbable. It’s as if the infants said to themselves: “Aha! There’s a less than .05 probability that this occurred by chance!”
The babies seemed to recognize whether the pingpong ball sample was random or not, but would they use that statistical pattern to actually test hypotheses and draw deeper conclusions? Would they, like Nate, be able to tell the difference between random noise and a genuine indication about how someone would act in the future?
Tamar Kushnir and colleagues did an experiment rather like the ping-pong ball one with 20-month-olds. An experimenter took out five toy frogs from a box of all frogs or she took five toy frogs from a box of almost all toy ducks. Then she left the room and an assistant gave the child a small bowl of frogs and a separate bowl of ducks. When she came back the experimenter exclaimed, “Just what I wanted! Can you give me some!” and put her hand out between the two bowls.
When she had taken frogs from a box of all frogs, children were equally likely to give her a frog or a duck. When she had taken frogs out of the box that was almost all ducks, children gave her a frog. The children seem to have figured out that the experimenter’s choices were just the result of random chance in the first case, but that she would consistently vote for frogs over ducks in the second. They used that discovery to predict what to give her next.
All this statistical brilliance raises a puzzle, of course. If kids are so smart, why are adults so stupid? Why aren’t we all like Nate? Of course, Nate Silver has much more data than the rest of us, and he analyzes it using more sophisticated tools than simple Bayesian inference itself. Moreover, he knows that he’s doing Bayesian analysis and the kids don’t—they just do it.
But I think there’s something deeper involved. Bayesian inference depends on the balance between “priors,” the beliefs we bring to a problem, and data. As we get older our “priors,” rationally enough, get stronger and stronger. We rely more on what we already know, or think we know, and less on new data. In some studies we’re doing in my lab now, my colleagues and I found that the very fact that children know less makes them able to learn more. We gave 4-year-olds and adults evidence about a toy that worked in an unusual way. The correct hypothesis about the toy had a low “prior” but was strongly supported by the data. The 4-year-olds were actually more likely to figure out the toy than the adults were.
As adults, the strength of our pre-existing beliefs, whether they involve the iniquities of Rasmussen or the malice of the MSM, may make those beliefs impervious to data. People often complain about the childishness of American politics. But maybe a bit more real childishness would be a good idea.