  We characterize Pareto optimality via "near" weighted utilitarian welfare
maximization. One characterization sequentially maximizes utilitarian welfare
functions using a finite sequence of nonnegative and eventually positive
welfare weights. The other maximizes a utilitarian welfare function with a
certain class of positive hyperreal weights. The social welfare ordering
represented by these "near" weighted utilitarian welfare criteria is
characterized by the standard axioms for weighted utilitarianism under a
suitable weakening of the continuity axiom.
