It changes the meaning, I think. In the second case, it means that snap judgements must be made to function, and they're, incidentally, based on shortcuts (but

It changes the meaning, I think. In the second case, it means that snap judgements must be made to function, and they're, incidentally, based on shortcuts (but you can leave out this part of the sentence), while in the first case 'on the basis of various shortcuts' is a very integral part of the information, and snap judgements must be made this way.