The theories screen off the theorists, so if we knew the theories then we could (given enough cleverness) decide based on the theories themselves what our belief should be.
But before we even look at the theories, you ask me which theory I expect to be correct. I expect the one which was written earlier to be correct. This is not because it matters which theory came first, irrespective of their content; it is because I have different beliefs about what each of the two theories might look like.
The first theorist had less data to work with, and so had less data available to insert into the theory as parameters. This is evidence that the first theory will be smaller than the second theory. I assign greater prior probabilities to small theories than to large theories, so I think the first theory is more likely to be correct than the second one.
The theories screen off the theorists, so if we knew the theories then we could (given enough cleverness) decide based on the theories themselves what our belief should be.
But before we even look at the theories, you ask me which theory I expect to be correct. I expect the one which was written earlier to be correct. This is not because it matters which theory came first, irrespective of their content; it is because I have different beliefs about what each of the two theories might look like.
The first theorist had less data to work with, and so had less data available to insert into the theory as parameters. This is evidence that the first theory will be smaller than the second theory. I assign greater prior probabilities to small theories than to large theories, so I think the first theory is more likely to be correct than the second one.