Compassion is sometimes the enemy of fairness. Take, for example, President Reagan's recent moving appeal for livers for several dying children.

Though the president's appeal was very moving, it obscures our collective failure to develop a coherent system that could help all people who need transplants, not just the few who succeed in gaining public attention. This failure is even conceded by Charles Fiske, who mounted a dramatic--and successful--media campaign last fall to get a life- saving liver for his 16-month-old daughter, Jamie.

This April he told a House committee he couldn't endorse the strategy he'd followed because media attention "may happen once or twice, but after a while may lose its effectiveness." Indeed, it already has-- now you need the president of the United States to get the public to respond to your need.

Moreover, focusing on particular patients leaves the false sense that the problem has been solved once the media reports that those folks have gotten the organs they needed. Instead of emotional appeals leading to an easy public catharsis, we need an ongoing commitment. Instead of Reagan playing the Great Communicator, we need his leadership as Chief Executive.

Relying on the ability of particular patients and their families to generate publicity is not only an unfair way of distributing organs. The spectacle of desperate families pushed into a media spotlight to save a sick relative is also contrary to the norms of medical privacy and human dignity, and interferes with patients and families making thoughtful decisions about which steps to take. Some aspects of organ transplantation are "accepted" and some are still "experimental," but all are complex, with substantial risks, and involve many novel elements and poorly understood long-term consequences.

Even the media-generated problems pale when compared with the needless deaths of patients who lack transplants from cadavers. Thousands of people die every year for the want of a kidney, and thousands more are added to the growing ranks of patients on long-term dialysis. And they're comparatively lucky --patients whose hearts or livers fail can't live for long, since in their cases no machines yet exist equivalent to the several forms of artificial kidney.

These deaths don't occur for want of potential cadaver organs. The best current estimate--taking account of the places where people die, the causes of death, difficulties in matching potential donors with recipients, and so forth--is that 12,000 Americans--1 percent of the total deaths each year-- could be potential donors. Though this would yield 24,000 kidneys (each body has two) only 3,425 cadaver kidneys were actually transplanted in 1981-- meaning that six-sevenths of the total that might have been available was not used.

The real value in the president's radio message was the encouragement he gave for filling out organ donor cards. These are simple, wallet-sized statements that permit people to give all or specific parts of their bodies for transplantation, research, or educational purposes upon death. Although provisions for donation through such cards has existed nationally for more than a decade many people are unaware of how easy-- and important--it is to have an organ card.

It's essential that physicians taking care of an accident victim know his or her wishes about organ donation, because organs must be transplanted immediately after death occurs to preserve their ability to function in the recipient's body. Yet many people who are willing to donate their organs don't carry donor cards. Some may even follow the Reagans' example--as reported by the First Lady's press secretary--and put their wishes into their wills, which will probably not be accessible in time to help with organ donation.

Fortunately, state anatomical gift laws also permit specified relatives to donate organs when a person hasn't made his or her wishes known before death. Since only a fraction of the population has filled out the cards, most donations result from decisions made by relatives at the time of death.

What could the administration do beyond dramatizing a few touching cases? First, the federal government could take several steps to increase organ donation itself, both by encouraging people to sign donor cards (for example, couldn't everyone entering military service be confronted with this choice, aye or nay?) and by coordinating and supporting programs aimed at the physicians and nurses who care for dying patients.

The one thing consistently found to improve the rate of organ donation is good education and support for the people who really have "access" to potential donors, namely physicians and nurses in intensive care units in hospitals. It's not an easy task to approach a family that's in grief--perhaps literally in shock--over the potential loss of a loved one and to ask them to shift their attention to other patients' need for organs.

The programs that educate and support health personnel successfully operate on a shoestring, so a little federal money would go a long way. And it would be money well spent from an economic as well as humane perspective if it enabled more patients with kidney, liver or heart failure to get an organ transplant that would end their need for other forms of medical care that are expensive but often not even lifesaving.

Besides helping volunteer groups to support "donor coordinators," the government could provide incentives for hospital cooperation and could aid in efforts already under way to have a nationwide 24-hour- a-day system for sharing organs among hospitals.

States should also be encouraged to end any lingering confusion over the "definition" of death. (This is a problem in many comatose, respirator cases, but it is particularly important when organs are going to be removed as soon as death is declared.) The problems can be solved by states' adopting the Uniform Determination of Death Act drafted by the President's Commission on Medical Ethics, the American Medical Association, the American Bar Association and the National Conference of Commissioners on Uniform State Laws. The act applies to all people, not just organ donors, but in such cases it assures physicians and family members that it is acceptable to diagnose death by measuring the cessation of brain functions while the heart and lungs are kept going artificially. The act has become law in 14 states since it was recommended in July 1981, and uniform adoption across the country should be encouraged.

We can hope that the president's concern will lead him beyond a few personal stories to instruct Health and Human Services Secretary Margaret Heckler to work with the health committees in Congress on developing a coordinated national effort that will let patients go to hospitals rather than newspapers when they need treatment. We can also hope that the difficult issue of how organ transplants are going to be paid for can be worked out more carefully than the legislative process a decade ago that overnight made end-stage kidney disease a special entitlement under Medicare-- and more fairly than the president's impulse that put Air Force jets at the disposal of the families involved in last week's liver transplants.