In light of a large number of patients requiring intensive care units (ICU), medical personnel and the health system must choose to try to save some lives and not others. In order to analyze this decision, the starting point is the contrast between Rawlsian positions and utilitarianism. On the one hand, the concepts of Rawls' contractualism, such as the original position, the veil of ignorance and the lexicographic order, could serve as parameters for a fair selection of principles for medical care protocols; and, on the other hand, the concept of classical utilitarianism with its emphasis on the greatest good and the consequences of actions as a parameter of justice. In conclusion, in the current situation, a utilitarian vision prevails, since it is proposed that the greatest number of lives and the greatest number of years of life should be saved, even if this means not caring for the elderly or people with comorbidities.