Hm on reflection I actually don’t think this does what I thought it did. Specifically I don’t think it captures the amount of ‘complexity barrier’ reducing the usability of the information. I think I was indeed equivocating between computational (space and time) complexity, vs. Kolmogorov complexity. My suggestion captures the later, not the former.
Also, some further Googling has told me that the expected absolute mutual information, my other suggestion at the end, is “close” to Shannon mutual information (https://arxiv.org/abs/cs/0410002) so doesn’t seem like that’s actually significantly different to the mutual information option which you already discussed.
Hm on reflection I actually don’t think this does what I thought it did. Specifically I don’t think it captures the amount of ‘complexity barrier’ reducing the usability of the information. I think I was indeed equivocating between computational (space and time) complexity, vs. Kolmogorov complexity. My suggestion captures the later, not the former.
Also, some further Googling has told me that the expected absolute mutual information, my other suggestion at the end, is “close” to Shannon mutual information (https://arxiv.org/abs/cs/0410002) so doesn’t seem like that’s actually significantly different to the mutual information option which you already discussed.