  We generalize the known equivalence between higher order gravity theories and
scalar tensor theories to a new class of theories. Specifically, in the context
of a first order or Palatini variational principle where the metric and
connection are treated as independent variables, we consider theories for which
the Lagrangian density is a function f of (i) the Ricci scalar computed from
the metric, and (ii) a second Ricci scalar computed from the connection. We
show that such theories can be written as tensor-multi-scalar theories with two
scalar fields with the following features: (i) the two dimensional sigma-model
metric that defines the kinetic energy terms for the scalar fields has
constant, negative curvature; (ii) the coupling function determining the
coupling to matter of the scalar fields is universal, independent of the choice
of function f; and (iii) if both mass eigenstates are long ranged, then the
Eddington post-Newtonian parameter has value 1/2. Therefore in order to be
compatible with solar system experiments at least one of the mass eigenstates
must be short ranged.
