In the New England Journal of Medicine, one Dr. Douglas Hanto has some advice ($) for anyone about to die for want of a kidney transplant, namely: shut up, get on the list, and wait your turn:
Given the shortage of transplantable organs, some potential recipients are going to great lengths to find organ donors on their own. For example, a patient with advanced liver cancer advertised on a personal Web site, billboards, and in the media for a liver, leading the family of a brain-dead donor to direct the donor's liver to him…The solicitation of families of deceased donors by recipients or their agents to direct the donation to a recipient other than the person at the top of the waiting list should not be permitted.
I'm far from an expert on organ donation from live donors, and the Satel/Postrel kidney tag team would surely have smarter things to say. So I'll just point out that this argument against letting people ask strangers for kidneys strikes me as completely vacuous:
A national conference report on nondirected living kidney donation provided support for a policy of nondirected donation to the list. On the basis of the results of a survey of adults in the United States whether donors should be able to choose their recipients, Spital reported that 93% of the respondents who were willing to donate a kidney to a stranger said they would still donate if they could not direct their donation.
So the vast majority of people who say they'd be willing to donate to a stranger say they'd be willing to donate to any stranger. Shocking but true: In a hypothetical situation, people do not prefer some hypothetical strangers over other hypothetical strangers. The only problem is that this survey question bears no relation to the way human beings actually relate to one another. The relevant question isn't "Will pre-existing donors chalk up a kidney for anyone at all?" but "Will solicitation encourage new donors?"
We know we empathize more strongly with individuals rather than anonymized masses of people; we're, in Paul Slovic's phrase in this month's Foreign Policy, "numbed by numbers." Organizations that solicit donors know this too, which is why they fill their sites with pictures of happy recipients. But "please give to some anonymous recipient who may resemble the person pictured here" is just not going to be as effective as a direct plea by a dying kid.
Addendum: Sally Satel has a sharp piece on incentives for donation in the Wall Street Jounal this very morning.