To each according to his needs: an axiomatic characterization

The age-old concept of allocating scarce resources according to “relative need” has proven notoriously difficult to formalize in a rigorous manner. This paper presents a new solution concept for this classical problem. After first providing a formal definition of what it means for one agent to be “everywhere needier than” another, we prove that the condition of being “needier than” is equivalent to being “more risk averse than”. Next, we introduce and axiomatize a scalar measure of “relative neediness”. This measure then becomes the basis for a needs-based allocation rule applicable to general n-person arbitration problems. The resulting allocation rule is closely related to the Nash bargaining solution, and does not entail explicit interpersonal comparisons of utility. In the final section, the new solution concept is embedded within a comprehensive theory of distributive justice.