I know of no satisfactory theory of literary (or indeed, any artistic) value. One might feel that the Divine Comedy is surely of greater value than an episode of Breaking Bad, but the proof of such discernment is elusive. For many years it was only too easy to blame the television fan for self-evident obtuseness while competing with other cognoscenti in appreciating the subtleties of Dante. In the past critics had no difficulty with the idea of the canon itself whatever negotiable differences they may have had over the exact list. The Romantics elevated Spenser, the Imagists liked Chinese lyric , and twentieth century found a worthy anticipation of metafiction in Tristram Shandy, but such adjustments occurred within a largely unquestioned structure. The critics of this bygone era were not wholly unlike religious scholars who, having settled on what to include in scripture, could then spend millennia commenting, interpreting, and interpreting the interpreters.
Though it worked well, this assumption was vulnerable. The acceptance of a canon was convenient, since the question of literary value seems ultimately like other matters of taste to lack much foundation apart from subjective impression. One may praise a wine with an elaborate flight of descriptors, while another finds the same taste unexciting. Two people may perceive the same characteristics and yet assign them different values. What may make a sauce seem elegant and subtle to one diner may be considered bland and boring to another. Tokay that once excited the highest praise from kings and popes now holds little interest for many drinkers. No one thinks that values in cuisine are nonexistent or wholly arbitrary, though food critics will differ among themselves after the broadest distinctions are made, and the more refined judgments may depend on extraordinary competence developed from experience. Criticism and comment are subsequent to impressions. Surely the situation is similar in literature.
Critics in the sense of the writers of reviews consider their primary responsibility to evaluate, to advise those who have found opportunity to read their remarks whether they would be well-advised to read the work under consideration. Such critics are necessarily free with value judgments, but their concern is not to present tightly reasoned proofs. This avoidance serves them well, since literary judgments,, like the first cause, are susceptible to the logical flaw of an infinite regress.  One may say a poem is great because of its concrete, specific imagery, yet whence comes the value of concreteness? Further, an ill-written poem may also passes the same sort of images, though clumsily phrased and ineptly utilized. A novel may be praised for its formal structure, yet use of analogous structure does not guarantee the success of another work of fiction. Surely the reader, no matter how knowledgeable, records a subjective impression and then cooks up a convincing basis for it.
One of the most acute critics of his generation, Northrup Frye came close to mystifying value with his emphatic statement: “The sense of value is an individual, unpredictable, variable, incommunicable, indemonstrable, and mainly intuitive reaction to literature.” 
Through history many critics have valued literature not so much for the aesthetic experience, the thrill of that “mainly intuitive reaction,” as for its extrinsic benefits. Its readers are thought by some to enjoy salutary effects such as a closer approach to truth, greater moral sensitivity, heightened social conscience, or some sort of vague increase in humanity. These judgments are wholly innocent of supportive reasoning or data. It may well be that few incarcerated felons have read Paradise Lost, but no one would regard the association between ignorance of Milton and committing crimes to be simply causal. This is unsurprising, given the fact that writers are expert in nothing other than the effective use of language; they are not specialists in religion or morality or politics, nor are they predictably more humane than most people, and the same can be said for their readers. Having studied a thousand Elizabethan sonnets, one will be familiar with the poetic form, language, and images, but will not necessarily be in any degree a better lover for his acquaintance with the poetry.
The fact is that literary value is dependent on the encounter of the individual reader with the text. No text can invariably produce a certain reaction in all readers, but such reactions are nonetheless quite real. A work will be called good or great if one is taken with its beauty (or, on the lower peaks of the Parnassian range, if one is amused or moved or entertained or thrilled or titillated). Over the centuries certain works have accumulated a record of admirers that reasonably suggest a new reader might likely be rewarded as predecessors have been.  When I left a performance of King Lear with tears in my eyes, my reaction was similar to countless viewers before me, though it may not have been shared by the person in the next seat. Thus literary value may be most rationally assigned, as indeed it has often been, by a consensus of competent consumers. Reasons may be detailed, but the judgment rests on the initial subjective reaction. The process is dynamic with minority opinion and idiosyncratic reactions always lobbying and jockeying like politicians for higher poll numbers.
As critics comment on a text, its significance grows. Eliot famously reminded readers of how comment can change the meaning of a work for the future and then his point was illustrated by his successful championing of the Metaphysicals. His appreciation for Donne gave new value to poems that had long been neglected. The Bible, an almost random miscellany of texts written over a long period of time, offers an example of a work which has gained value due to being closely read for millennia, resulting in richly developed interconnections and implications. What is more, they have yielded an immense hermeneutic harvest while being read (albeit only by Christians) as a unified work. The value is clearly constituted in the consumption.
The issue of value has a particular value in the present era since “cultural criticism” and the like have largely exiled considerations of value from the academy.  Yet who can read without value judgments? From my youth until today, my study was motivated by the intention to spend my time in contemplation of the best writing (and the second-best). Something of the same motive must be common to virtually all devotees of literature. The fact that the basis for such distinctions may be elusive and that estimates of worth may never elicit unanimous agreement does not invalidate them.
The chief difference between taste in poetry and in other areas is that art is so subtle a carrier of meaning, so dense a pattern of signification, that it conveys far more precise and detailed a record of human consciousness than can taste in food or clothing or home décor. Apart from fabulous complexity, different works may have widely varying aims. For one author human psychology is the focus, while another may aim to present lovely landscapes lushly sketched; a third may seek to convey some insight into lived experience, a fourth to pipe the most captivating melody, the fifth to evoke laughter, and on and on. Each must be judged by its aims, but none is inherently superior or inferior to others. Each presents a separate case and can only be evaluated on the basis of the encounter of an author and reader, each unique but sharing much as well. While judgments of taste can never be proven, they are nonetheless the starting point of literary studies. Just as the Greeks considered praise and blame the very basis of considering people’s lives, literary value is at once the motive (in prospect) and the end (in experience) of considering the literature people produce.
1. The general philosophical problem is well-formulated by Sextus Empiricus, part of Agrippa’s trilemma according to Diogenes Laertius.
2. From “On Value-Judgments,” Contemporary Literature Vol. 9, No. 3, Summer, 1968, 311-318. The essay was later reprinted in The Stubborn Structure 1970. Frye’s direct engagement of the issue and his forthright statement exemplify his practice. He was a pioneer in the systematic analysis of literature, and his Anatomy of Criticism earns its title. Apart from theory, his work is full of brilliant specific comments. Frye is uneasy here, however, and he hedges this apparently unqualified characterization of literary value by saying in the same essay that greater knowledge can produce more accurate judgments. But what is the standard of accuracy?
3. This strikes me as similar to the way physicists tell us physical reality is best considered “a wave of probability.”
4. For an energetic response see James Seaton’s Literary Criticism from Plato to Post-Modernism: The Humanistic Alternative. My review “On the Proper Ends of Literary Study” appears on this site.