  We reconsider, from a novel perspective, how unitarity constrains the
corrections to the ratio of shear viscosity \eta\ to entropy density s. We
start with higher-derivative extensions of Einstein gravity in asymptotically
anti-de Sitter spacetimes. It is assumed that these theories are derived from
string theory and thus have a unitary UV completion that is dual to a unitary,
UV-complete boundary gauge theory. We then propose that the gravitational
perturbations about a solution of the UV complete theory are described by an
effective theory whose linearized equations of motion have at most two time
derivatives. Our proposal leads to a concrete prescription for the calculation
of \eta/s for theories of gravity with arbitrary higher-derivative corrections.
The resulting ratio can take on values above or below 1/4\pi\ and is consistent
with all the previous calculations, even though our reasoning is substantially
different. For the purpose of calculating \eta/s, our proposal also leads to
only two possible candidates for the effective two-derivative theory: Einstein
and Gauss-Bonnet gravity. The distinction between the two is that Einstein
gravity satisfies the equivalence principle, and so its graviton correlation
functions are polarization independent, whereas the Gauss-Bonnet theory has
polarization-dependent correlation functions. We discuss the graviton
three-point functions in this context and explain how these can provide
additional information on the value of \eta/s.
