I tied asking this question a different way over at the philospohy stackexchange, but I think I want to ask it in a more formal way.
If I understand Solomonoff induction correctly, given two hypotheses which have been able to accurately predict a data set, the hypothesis with the lower Kolmogorov complexity is the one which is more likely to produce a correct prediction for the next data point.
Would it be reasonable to say that a hypothesis with a higher Kolmogorov complexity is more easily falsified? It seems that the answer is yes, since it has a lower probability of correctly predicting the next data point in the sequence.
Also, can something be said about relative complexity when one program generates more than just the data set in question? For instance,
A: y = 2x
B: y ∝ x
for say {(1, 2)}. The reason I am asking is because I am curious about cases when one hypothesis implies the other. A implies B and it seems like B is less "complex" than A. But this measure of complexity may be incompatible with the concepts in Solomonoff induction.
Suggested edits are welcome. Thank you.