We analyse individuals' preferences vaccine-distribution schemes in the World, the EU, and their country of residence that emphasise circumstances rather than outcomes or effort. We link preferences to previously-measured cognition, and find that high-cognition individuals are 35% more likely to always support such schemes. These preferences are not driven by scheme convenience nor vaccine hesitancy, but appear to be caused by prosociality. We argue that this latter is linked to the perception of less equality of opportunity in society: despite having similar ideals about the role that effort and luck should play in life, high-cognition individuals perceive outcomes to be more determined by luck.