We examine the implications for social choice of individuals having an intrinsic sense of fairness. Taking the viewpoint that social justice reflects the moral attitudes of the constituent members, we analyze the effect of the intensity of the individual sense of fairness on university admission policies. Assuming that these policies are determined by bargaining over test scores to be used as cut-off points for admission of members of diverse social groups show that, in general, a more intense sense of fairness of the members of a group leads to an admission policy that is more compatible with their idea of fairness. Consequently, a society whose members have a common notion tends to implement fairer admission policies when the intensity of the sense of fairness of individual memebrs increase. This is even if the policies are ultimately determined by the bargaining power of the different groups.