Friedman's "Prediction vs. Explanation"

Eliezer Yudkowsky

We do ten experiments. A scientist observes the results, constructs a theory consistent with them, and uses it to predict the results of the next ten. We do them and the results fit his predictions. A second scientist now constructs a theory consistent with the results of all twenty experiments.

The two theories give different predictions for the next experiment. Which do we believe? Why?

One of the commenters links to Overcoming Bias, but as of 11PM on Sep 28th, David's blog's time, no one has given the exact answer that I would have given. It's interesting that a question so basic has received so many answers.

David D. Friedman asks:

We do ten experiments. A scientist observes the results, constructs a theory consistent with them, and uses it to predict the results of the next ten. We do them and the results fit his predictions. A second scientist now constructs a theory consistent with the results of all twenty experiments.

The two theories give different predictions for the next experiment. Which do we believe? Why?

Let's suppose, purely for the sake of argument of course, that the scientists are superrational.

The first scientist chose the most probable theory given the 10 experiments. If the predictions are 100% certain then it will still be the most probable after 10 more successful experiments. So, since the second scientist chose a different theory, there is uncertainty and the other theory assigned an even higher probability to these outcomes.

In reality people are bad at assessing priors (hindsight bias), leading to overfitting. But these scientists are assumed to have assessed the priors correctly, and given this assumption you should believe the second explanation.

Of course, given more realistic scientists, overfitting may be likely.

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Friedman's "Prediction vs. Explanation"

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Friedman's "Prediction vs. Explanation"

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