According to John Rawls, maximin, which requires that the economic situation of the most underprivileged should be maximized, is one of the fundamental principles of social justice. Based on three scenarios which attempt to place respondents behind a "veil of ignorance", a French survey (PISJ, 2009) and an Italian survey (OSCF, 2016) conducted on representative quota-based samples show that support for this principle considerably outweighs support for strong equality and the maximization of total or average wealth. In addition, this choice transcends many sociodemographic or ideological divisions. The respondents were, however, much more undecided about which is more just: a society in which the poorest members are more numerous but richer or a society in which the poorest members are fewer in number but poorer. The robustness of the findings is confirmed by the similarity between the results from France and Italy.