Friday, December 07, 2007

The human mind intuits probability at one year of age.

This interesting work (PDF here) shows that 12 month old infants have expectations about future single events never before seen, based on their likelihood. The authors presented movies in which three identical objects and one different in color and shape bounced randomly inside a container with an open pipe at its base, as in a lottery game. After 13 s, an occluder hid the container and one object, either one of the three identical objects (probable outcome) or else the different one (improbable outcome), exited from the pipe. The infants looked significantly longer when they witnessed the improbable outcome.

The authors also show that it only after ~3 years of age that children can overrule their probabilistic intuition when an experienced frequency of outcome disagrees with prior probability.

The article's introduction (slightly edited) sets the context for the work:
Rational agents should integrate probabilities in their predictions about uncertain future events. However, whether humans can do this, and if so, how this ability originates, are controversial issues. One influential view is that human probabilistic reasoning is severely defective, being affected by heuristics and biases. Another influential view claims that humans are unable to predict future events correctly without experiencing the frequency of past outcomes. Indeed, according to this view, in the environment in which we evolved only "the encountered frequencies of actual events" were available, hence predicting the probability of an event never before observed is meaningless.

A third, largely unexplored view is that intuitions about possible future events ground elementary probabilistic reasoning. Against this view, several classic, although not unchallenged, studies seemingly show that probabilistic reasoning appears late in development and requires frequency information. However, if, as Laplace wrote, probability theory "makes us appreciate with exactitude that which exact minds feel by a sort of instinct", humans must have intuitions about probabilities early in their life. The present work supports this view.


  1. I'm disappointed that I can't read the original article (don't have a PNAS subscription).

    I'm not sure I understand the protocol very well. In the image you posted, the blue objects are traveling along trajectories that would be more likely to exit the enclosure and the yellow object would be less likely to do so? If the enclosure and three of the objects are occluded, how do they know that the increase in looking time is due to the probability of exiting the enclosure, or in the case of the yellow object remaining, a case of novelty detection? In other words, how do they know the infants weren't just staring longer because the novel stimuli remained on screen? Why not use four objects that are all the same color?

    And in these sorts of infant looking-time paradigms, I'm always skeptical about claims of innateness. Is that what the authors are pushing here? Even if the infant has not been exposed to this exact stimuli, surely by the time they are 1 year-old they have been exposed to quite a lot of things moving in the real world, enough to be able to construct probabilistic models.

  2. The article has links to movies showing the stimuli. I don't think they are pushing the innateness angle, intuiting probability could possible rise out of the logic of learning and developing hand-eye coordination, or whatever. I'm going ahead and putting a link to the PDF file in the post.