  This work deals with the implementation of social choice rules using dominant
strategies for unrestricted preferences. The seminal Gibbard-Satterthwaite
theorem shows that only few unappealing social choice rules can be implemented
unless we assume some restrictions on the preferences or allow monetary
transfers. When monetary transfers are allowed and quasi-linear utilities
w.r.t. money are assumed, Vickrey-Clarke-Groves (VCG) mechanisms were shown to
implement any affine-maximizer, and by the work of Roberts, only
affine-maximizers can be implemented whenever the type sets of the agents are
rich enough.
  In this work, we generalize these results and define a new class of
preferences: Preferences which are positive-represented by a quasi-linear
utility. That is, agents whose preference on a subspace of the outcomes can be
modeled using a quasi-linear utility. We show that the characterization of VCG
mechanisms as the incentive-compatible mechanisms extends naturally to this
domain. Our result follows from a simple reduction to the characterization of
VCG mechanisms. Hence, we see our result more as a fuller more correct version
of the VCG characterization.
  This work also highlights a common misconception in the community attributing
the VCG result to the usage of transferable utility. Our result shows that the
incentive-compatibility of the VCG mechanisms does not rely on money being a
common denominator, but rather on the ability of the designer to fine the
agents on a continuous (maybe agent-specific) scale.
  We think these two insights, considering the utility as a representation and
not as the preference itself (which is common in the economic community) and
considering utilities which represent the preference only for the relevant
domain, would turn out to fruitful in other domains as well.
