Title’s an oxymoron, of course.
Still, it’d be nice to do better than a subjective, personal good-book-feeling, or an authoritarian canon handed down from on-high. Complicating this is the fact that quality is inherently subjective – but humans aren’t really all that different from each other, compared to two random minds in mind-space. So it’s a bit too early to throw up our hands and say “it’s impossible!”: we should be able to quantify likeability-to-humans-in-general, since humans-in-general are clearly a category with a certain amount of psychological unity.
(On a side note, it’s almost always too early to say something’s impossible.)
The first thought is: well, a book might by coincidence have quality with respect to a single person. But it’s much less likely for it to have quality with respect to a few million, if it’s by pure chance. So popularity works, to a first order approximation.
Honestly, we could stop here; as much as I may personally find it distasteful, clearly there is something that sets Twilight apart from other works, because those other don’t appeal to as many people. But post-modernism aside, there does seem to be a sense in which Shakespeare, the Kojiki, the Romance of the Three Kingdoms are all “better” than, say, Twilight. The obvious difference seems to be diversity: Twilight has a very narrow demographic, if a large one, while Shakespeare and the Romance have fans in every walk of life over centuries.
Which really boils down to our original problem of subjectivity: if you average “I-like-this-book”-ness over a bunch of people who are mostly the same, that’s not going to be a good measure of quality-with-respect-to-humanity as a whole.
Which leads us to a result that, honestly, we could’ve seen coming: define “quality” as a function of popularity and diversity. A work has high quality if it appeals to many people in many groups; a work has medium quality if it only appeals to a single class of people, but has high appeal within that demographic; a work is low quality if nobody likes it at all. Which, as we would like for a designed metric, nicely reproduces our intuition: Shakespeare, popular over centuries, is high quality; Harry Potter, popular worldwide but only in the past few decades, is medium-high; Twilight, very popular in a narrow demographic, is medium quality; and Tweet #24234, which nobody actually cares about, is low quality.
(An easy test: the higher the quality, the more likely a random human is to like it. Go take a work of Shakespeare to a culture that remains insular – say, a random tribe in the Congo – and see if they like it, even if they “miss the point” due to cultural differences; compare, say, Twilight. To the first, at least, I can cite Shakespeare in the Bush.)