So we could quibble over the details of Friston 2009, *buuuuut*...
I don’t find it useful to take Friston at 110% of his word. I find it more useful to read him like I read all other cognitive modelers: as establishing a language and a set of techniques whose scientific rigor he demonstrates via their application to novel experiments and known data.
He’s no more an absolute gold-standard than, say, Dennett, but his techniques have a certain theoretical elegance in terms of positing that the brain is built out of very few, very efficient core mechanisms, applied to abundant embodied training data, instead of very many mechanisms with relatively little training or processing power for each one.
Rather than quibble over him, I think that this morning in the shower I got what he means on a slightly deeper level, and now I seriously want to write a parody entitled, “So You Want to Write a Friston Paper”.
>”If I value apples at 3 units and oranges at 1 unit, I don’t want at 75%/25% split. I only want apples, because they’re better! (I have no diminishing returns.)”
I think what I’d have to ask here is: if you only want apples, why are you spending your money on oranges? If you will not actually pay me 1 unit for an orange, why do you claim you value oranges at 1 unit?
Another construal: you value oranges at 1 orange per 1 unit because if I offer you a lottery over those and let you set the odds yourself, you will choose to set them to 50⁄50. You’re indifferent to which one you receive, so you value them equally. We do the same trick with apples and find you value them at 3 units per 1 apple.
I now offer you a lottery between receiving 3 apples and 1 orange, and I’ll let you pay 3 units to tilt the odds by one expected apple. Since the starting point was 1.5 expected apples and 0.5 expected oranges, and you insist you want only 3 expected apples and 0 expected oranges, I believe I can make you end up paying more than 3 units per apple now, despite our having established that as your “price”.
The lesson is, I think, don’t offer to pay finite amounts of money for outcomes you want literally zero of, as someone may in fact try to take you up on it.