Here is my answer without looking at the comments or indeed even at the post linked to. I’m working solely from Eliezer’s post.
Both theories are supported equally well by the results of the experiments, so the experiments have no bearing on which theory we should prefer. (We can see this by switching theory A with theory B: the experimental results will not change.) Applying bayescraft, then, we should prefer whichever theory was a priori more plausible. If we could actually look at the contents of the theory we could make a judgement straight from that, but since we can’t we’re forced to infer it from the behavior of scientist A and scientist B.
Scientist A only needed ten experimental predictions of theory A borne out before he was willing to propose theory A, whereas scientist B needed twenty predictions of theory B borne out before he was willing to propose theory B. In absence of other information (perhaps scientist B is very shy, or had been sick while the first nineteen experiments were being performed), this suggests that theory B is much less a priori plausible than theory A. Therefore, we should put much more weight on the prediction of theory A than that of theory B.
If I’m lucky this post is both right and novel. Here’s hoping!
Here is my answer without looking at the comments or indeed even at the post linked to. I’m working solely from Eliezer’s post.
Both theories are supported equally well by the results of the experiments, so the experiments have no bearing on which theory we should prefer. (We can see this by switching theory A with theory B: the experimental results will not change.) Applying bayescraft, then, we should prefer whichever theory was a priori more plausible. If we could actually look at the contents of the theory we could make a judgement straight from that, but since we can’t we’re forced to infer it from the behavior of scientist A and scientist B.
Scientist A only needed ten experimental predictions of theory A borne out before he was willing to propose theory A, whereas scientist B needed twenty predictions of theory B borne out before he was willing to propose theory B. In absence of other information (perhaps scientist B is very shy, or had been sick while the first nineteen experiments were being performed), this suggests that theory B is much less a priori plausible than theory A. Therefore, we should put much more weight on the prediction of theory A than that of theory B.
If I’m lucky this post is both right and novel. Here’s hoping!