What does Ursula Le Guin base happiness off of in "The Ones Who Walk Away from Omelas"?

In Ursula K. Le Guin's short story "The Ones Who Walk Away From Omelas," the third-person narrator is an outsider (like the reader), but one who seems to know a lot about the city of Omelas. There are also clues throughout the story that Omelas is a theoretical or fantastical city (even in the world of the story), because the narrator allows some room for interpretation and creation on the part of the reader.
With this in mind, the narrator explains the concept of happiness in Omelas in a complex and contradictory (or ironic) way. This allows for the greater impact of the twist at the end, where we find out that the splendor of the city is all at the expense of one child tortured in a basement. The narrator guides the reader toward making our own moral judgments, much as the ones who walk away from Omelas at the end of the story do.
Here are some important ways that the narrator describes happiness in the city of Omelas:

The trouble is that we have a bad habit, encouraged by pedants and sophisticates, of considering happiness as something rather stupid. Only pain is intellectual, only evil interesting.... But to praise despair is to condemn delight, to embrace violence is to lose hold of everything else.... They were mature, intelligent, passionate adults whose lives were not wretched. O miracle!

This quote comes after the narrator describes the seemingly faultless splendor of Omelas, and declares that the people of the city were happy, and how misunderstood (and undervalued) happiness is as a concept. The irony of this introduction to Omelas's happiness is that we will later learn that it apparently depends entirely on the degradation of a child (violence and evil indeed).

Happiness is based on the just discrimination of what is necessary, what is neither necessary nor destructive, and what is destructive.

The narrator uses this statement to explain why Omelas has certain technologies but not others. They can have public transport but not cars, for example, because the former falls into the middle category. The interesting part of this quote is how it explains the way that the people of Omelas have justified their foundational crime. They haven't been able to make a "just discrimination" between these three things, because rather than seeing the torture of the child as "destructive," they instead view it as "necessary." This shows the flaw in not just their justice, but also their happiness.

Their tears at the bitter injustice dry when they begin to perceive the terrible justice of reality, and to accept it. Yet it is their tears and anger, the trying of their generosity and the acceptance of their helplessness, which are perhaps the true source of the splendor of their lives. Theirs is no vapid, irresponsible happiness. They know that they, like the child, are not free. They know compassion.

This quote comes toward the end of the story, when the narrator tells us about the tortured child and how everyone in the city must go and see the child when they are young, in order to understand the foundation of their society. The narrator describes the anguish the young people feel and then this process of acceptance almost all of them go through. This is definitely the point in the story when the morality gets muddled. The narrator is trying—as rationally as possible—to describe the reasoning behind the torture of the child. But the reader is meant to think back on those previous moments when happiness was explained and to see how this contradicts those explanations, as well as how the acceptance of this injustice magnifies the injustice.
The happiness of the people of Omelas is based—foundationally—on the torture of one child. They believe that the two are so inextricably linked that if they were to bring the child up out of that place, they would "throw away the happiness of thousands for the chance of the happiness of one."