Strategy-proofness and weighted voting

A strict social welfare function (SSWF) that always yields an asymmetric binary relation with a single maximal alternative induces a social choice rule on its domain. It is known that if the induced rule is strategy-proof then it can also be generated by a SSWF satisfying non-reversal. This paper proves that a SSWF satisfying anonymity and IIAsatisfies non-reversal if and only if it is a weighted voting rule. If there are less than six voters then a SSWF satisfying neutrality and IIA satisfies non-reversal if and only if it is a weighted voting rule, but this equivalence does not hold for more than five voters.