Weighted Utilitarianism over Finite Streams

We provide an axiomatic analysis of weighted utilitarianism from which many available characterizations follow. We show that a social preference order over finite utility streams has a weak weighted utilitarian representation if it satisfies the axioms of Weak Pareto, Minimal Individual Symmetry, and Shift Invariance. This result can be strengthened to yield a strong (that is, complete) weighted utilitarian representation if and only if it satisfies the above three basic axioms, and an axiom on the “continuity of indifference”. Unlike many available characterizations, our result directly constructs the social welfare weights (used in the above weighted utilitarian representation results) from the preference order. Moreover, the welfare weights are uniquely identified allowing for comparative statics analysis. We show with an example that the three basic axioms do not guarantee a representation (and therefore a weighted utilitarian representation) of the preference order.