What theory of justice would most likely approve of an equal distribution of goods such as money or shelter?

Distributive justice

Explanation:

Distributive justice describes the idea that resources should be justly allocated. Distributive justice is studied in philosophy, social sciences. In psychology, distributive justice is described as fairness in distribution of rewards and costs among group members or society such as when workers are rewarded according to how many hours they work. It is different from just process which is involved with how law is administered-just or unjust.