A child dying of cystic fibrosis now has a shot at a lung transplant. A federal judge in Pennsylvania has ordered the Department of Health and Human Services to let 10-year-old Sarah Murnaghan move from waiting list for lungs from deceased children to the waiting list for lungs from adults.

The federal organ rationing system had previously limited transplants from adult donors to patients more than 12 years old. Sarah’s parents argued that federal law requires organs to be rationed based on the severity of a patient’s condition and “the unique health care needs of children,” implying that adults can be denied organs from children but not vice versa. Although some child transplant candidates’ bodies are too small to accept organs from adults, Sarah’s doctors say that would not be a problem for her.

The pool of available lungs from adult donors, the Murnaghans argued, is 50 times greater than the number from children. There are currently 14 children and 148 adults waiting for lungs in Pennsylvania. Ten Pennsylvania children and 42 adults have been waiting longer than a year for a matching organ.

The case points up the tragic and, despite efforts to the contrary, inherently arbitrary nature of organ allocation. As long as there is an absolute shortage of organs, giving one person a transplant means denying it to someone else.

Contrary to what many people assume, merely signing an organ donor card doesn’t mean your organs will be transplanted when you die. You have to die in exactly the right way, and very few people do. The shortages are especially acute for pediatric organs since, fortunately, relatively few children die from massive brain trauma. The separate pediatric and adult lists reflect the need to make sure those rare organs go to children who can’t tolerate transplants from adult.

Murnaghan’s family is correct that the 12-year-old cutoff doesn’t reflect medical considerations and, as a result, puts children like Sarah at an arguably unfair disadvantage. But any weighing of lives will seem unfair to the losers. The current system generally favors people in dire straits over healthier patients, for instance. It gives patients points for waiting a long time and, as a result, favors older, sicker patients over younger, healthier ones. That reflects one politically determined idea of fairness. But it would be equally fair-- or equally unfair -- to favor healthier patients who might live longer with the precious organ.

A sick little girl makes a compelling story. The tragedy is that if little Sarah gets her lung, someone else will go without.

(Virginia Postrel is a Bloomberg View columnist. Follow her on Twitter.)