On social welfare orders satisfying anonymity and asymptotic density-one Pareto

We study the nature (constructive versus non-constructive) and the issue of real-valued representability of social welfare orders, on the set of infinite utility streams, satisfying the anonymity and asymptotic density-one Pareto axioms. We characterize the existence of representable and constructive social welfare orders (fulfilling the aforementioned axioms) in terms of easily verifiable conditions on the feasible set of one-period utilities, denoted by Y⊂R: a social welfare order satisfying anonymity and asymptotic density-one Pareto is representable and admits explicit description if and only if Y contains finitely many elements.