  We consider dominant strategy implementation in private values settings, when
agents have multi-dimensional types, the set of alternatives is finite,
monetary transfers are allowed, and agents have quasi-linear utilities. We show
that any implementable and neutral social choice function must be a weighted
welfare maximizer if the type space of every agent is an $m$-dimensional open
interval, where $m$ is the number of alternatives. When the type space of every
agent is unrestricted, Roberts' theorem with neutrality \cite{Roberts79}
becomes a corollary to our result. Our proof technique uses a {\em social
welfare ordering} approach, commonly used in aggregation literature in social
choice theory. We also prove the general (affine maximizer) version of Roberts'
theorem for unrestricted type spaces of agents using this approach.
