Some philosophers and physicians have argued that alcoholic patients, who are responsible for their liver failure by virtue of alcoholism, ought to be given lower priority for a transplant when donated livers are being allocated to patients in need of a liver transplant. The primary argument for this proposal, known as the Responsibility Argument, is based on the more general idea that patients who require scarce medical resources should be given lower priority for those resources when they are responsible for needing them and when they are competing with patients who need the same resources through no fault of their own. Since alcoholic patients are responsible for needing a new liver and are in direct competition with other patients who need a new liver through no fault of their own, it follows that alcoholic patients ought to be given lower priority for a transplant. In this article, I argue against the Responsibility Argument by suggesting that in order for it to avoid the force of plausible counter examples, it must be revised to say that patients who are responsible for needing a scarce medical resource due to engaging in behavior that is not socially valuable ought to be given lower priority. I'll then argue that allocating organs according to social value is inconsistent or in tension with liberal neutrality on the good life. Thus, if one is committed to liberal neutrality, one ought to reject the Responsibility Argument.