On Social Welfare Orders Satisfying Anonymity and Strong Equity

This paper studies the nature (representation and construction) of social welfare orders on infinite utility streams, satisfying strong equity and anonymity. We show: 1) there does not exist a social welfare function satisfying the axioms of Anonymity, Monotonicity and Strong Equity for every non-trivial domain Y (i.e., any domain Y containing at least four distinct elements); 2) there exists a social welfare function satisfying the axioms of Anonymity, Strong Equity (and Weak Dominance); 3) any social welfare order satisfying Anonymity and Strong Equity somehow requires the axiom of choice, so in a sense is non-constructive