# Optimization Rendering of Distributive Justice

P is population under governance.

L is the available policies or laws that can be put into practice and enforcement.

Let there be a utility function $u(p,l)$ for each individual $p\in P$‘s benefit under political system $l\in L$. Furthermore let the function be polymorphic and accepts $u(p\prime, l)$ where $p\prime \subseteq P$

Let the government have the sole objective of optimization of some utility of its people, then Utilitarian says the desired governance chooses

$\mathop{argmax}_{l\in L}{u(P,l)}$

And furthermore, they define that

$u(P,l) =\sum_{p\in P}u(p,l)$

The rowlsian would stipulate that selection should be

$argmax_{l\in L}{(argmin_{p\in P}u({p,l}))}$

It imposes this procedural restrictions on the family of allowable $L$ to mean those that satisfy “equality of opportunity.”

This rendering largely based on Michael Snadel’s Justice class on edX.