In "The Ones Who Walk Away From Omelas" by Ursula Le Guin, what dilemma do the citizens of Omelas face?

In Le Guin's "The Ones Who Walk Away from Omelas," the society presented is a Utopia built upon the back of one miserable, abused, neglected, and caged child.  So the choice is to maintain the Utopia or give it up to rescue its sacrificial victim, this child. 

Most of the people of Omelas are shown this victim when they are between the ages of eight and twelve, and it is explained to them what purpose...

In Le Guin's "The Ones Who Walk Away from Omelas," the society presented is a Utopia built upon the back of one miserable, abused, neglected, and caged child.  So the choice is to maintain the Utopia or give it up to rescue its sacrificial victim, this child. 

Most of the people of Omelas are shown this victim when they are between the ages of eight and twelve, and it is explained to them what purpose this poor, wretched being serves, the happiness and prosperity of all.  The child must remain neglected and caged, and "there may not be even a kind word spoken to the child" (Le Guin 4).  People are trouble by this, but they rationalize.  The damage is already done, and it would thus be pointless to rescue this child.  It's too late to save him or her, so they enjoy the perfect weather, the dances, the parades, and all the pleasures life in Omelas brings. 

A very few find this unbearable and they are the ones whom the title refers to. They walk away.  They never return.  But they "seem to know where they are going" (4).  They are more ethical, certainly, than those who remain, declining to enjoy happiness at the cost of even one child in misery. 

There is a theory of ethics called utilitarianism, which posits that given a choice between competing harms, one should choose to save the person or people who will do the most good for the most people.  This story takes utilitarianism to a whole new level, one never contemplated, I would guess, by John Stuart Mill. 

This story always makes for an interesting thought experiment.  You might want to ask yourself what you would do in these circumstances.  You might remain. Or you might be one of the ones who walks away.