  We put forward the idea that all the theoretically consistent models of
gravity have contributions to the observed gravity interaction. In this
formulation, each model comes with its own Euclidean path-integral weight where
general relativity (GR) has automatically the maximum weight in high-curvature
regions. We employ this idea in the framework of Lovelock models and show that
in four dimensions the result is a specific form of the $f(R,G)$ model. This
specific $f(R,G)$ satisfies the stability conditions and possesses
self-accelerating solutions. Our model is consistent with the local tests of
gravity since its behavior is the same as in GR for the high-curvature regime.
In the low-curvature regime the gravitational force is weaker than in GR, which
can be interpreted as the existence of a repulsive fifth force for very large
scales. Interestingly, there is an intermediate-curvature regime where the
gravitational force is stronger in our model compared to GR. The different
behavior of our model in comparison with GR in both low- and
intermediate-curvature regimes makes it observationally distinguishable from
$\Lambda$CDM.
