  We investigate optimization models for the purpose of computational
redistricting. Our focus is on nonconvex objectives for estimating expected
black voter and political representation. The objectives are a composition of a
ratio of variables and a normal distribution's cumulative distribution function
(or "probit curve"). We extend the work of Validi et al.
\cite{validi2020imposing}, which presented robust implementation of contiguity
constraints. By developing mixed integer linear programming models that closely
approximate the nonlinear model, our approaches yield tight bounds on these
optimization problems and we exhibit their effectiveness on county-level data.
