Welfare egalitarianism in non-rival environments

We study equity in economies where a set of agents commonly own a technology producing a non-rival good from their private contributions. A social ordering function associates to each economy a complete ranking of the allocations. We build social ordering functions satisfying the properties that individual welfare levels below the stand-alone lower bound (respectively, above the unanimity upper bound) should be increased (respectively, reduced). Combining either property with efficiency and robustness properties with respect to changes in the set of agents, we obtain a kind of welfare egalitarianism based on a constructed numerical representation of individual preferences.