  Higher derivative theories of gravity are associated with a mass scale to
insure the correct dimensionality of the covariant derivatives. This mass scale
is known as the scale of non-locality. In this paper, by considering a higher
derivative toy model, we show that for a system of $n$ particles the effective
mass scale is inversely proportional to the square root of the number of
particles. We demonstrate that as the number of particles increases the
corresponding effective mass scale associated with the scattering amplitude
decreases.
