This paper shows that, if the performance of the economy is independen
t of the identities of individuals, then many welfare criteria yield s
ets of optimal social states that are equal to the Pareto optimal set.
This result is proved for income distributions and extended to more g
eneral social choice problems. If the independence condition holds, th
en the set of optimal states is invariant to the adoption of an anonym
ity axiom, and to the utility information available.