Short answers, pulled from the story.
Distributive justice concerns the fair allocation of resources, goods, and opportunities across a society. In social psychology it is specifically defined as the perceived fairness of how rewards and costs are shared among group members. Most contemporary theories assume material scarcity as a starting condition.
Donelson R. Forsyth identified five distributive norms: equality (equal shares regardless of contribution), equity (outcomes proportional to inputs), power (more for those with authority), need (more for those with the greatest shortfall), and responsibility (those with the most share with those who have less).
The veil of ignorance is a concept from John Rawls's book A Theory of Justice. It describes a hypothetical condition in which people choose the rules of society without knowing their own social position, talents, or objectives. The veil is designed to remove personal bias so that negotiators protect all members of society, including the least advantaged.
Friedrich von Hayek argued that distributive justice is meaningless in a free market society because market outcomes arise from spontaneous individual interactions, not deliberate design, making it incoherent to call them just or unjust. He also held that achieving any specific distributive outcome is impossible because it would require gathering all individual information into a single planning effort. His views were developed most fully in The Road to Serfdom.
Robert Nozick's Entitlement Theory, set out in Anarchy, State, and Utopia, holds that a distribution is just if it results from just acquisition and just voluntary exchange. He rejected any external standard of equality or need as grounds for overriding distributions that arose through legitimate individual transactions.
In environmental contexts, distributive justice concerns the equitable distribution of technological and environmental risks, impacts, and benefits. Evidence shows that burdens such as exposure to hazardous waste, land appropriation, and armed violence fall disproportionately on the Global South, while benefits concentrate in the Global North.