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.

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