# Set of utilitarian weights

I am wondering if there are literature which studies specific properties of the set of utilitarian weights?

To be more specific, when we have some axioms that characterize the preference of a social planner (and gives a utility representation), we can usually say the set of utilitarian weights is convex and closed. But are there previous papers studying more properties about the set?

I am grateful if some one can point me out some related paper regarding properties of set of utilitarian weights.

One is Relative Utilitarianism (RU). Under the axioms below, society's preference can be represented by the simple sum of individuals' vNM utilities (each normalized to between $0$ and $1$). That is, every individual is given equal weight.
1. Pareto Axiom. (This is just the usual: If everyone prefers lottery $p$ to $q$, then so too does society. And if everyone strictly prefers lottery $p$ to $q$, then so too does society.)