Generalized raking is a method to estimate weights for a survey so that population totals are satisfied exactly.
In Section 2 of both Deville and Särndal (1992) and Deville et al. (1993), a distance function $G$ between design and estimated weights is used. The procedure is generic, but $G$ needs to fulfill some basic prerequisites. In particular, it must be nonnegative, strictly convex, and evaluate to zero for $x=1$. Furthermore, $G^{\prime\prime}(1) = 1$ is required.
I'm having trouble understanding the last requirement. Both papers simply state it, but I haven't found where this requirement is actually used. Is it to assure convergence of Newton's method that is used for finding the solution?