  We propose three novel gerrymandering algorithms which incorporate the
spatial distribution of voters with the aim of constructing gerrymandered,
equal-population, connected districts. Moreover, we develop lattice models of
voter distributions, based on analogies to electrostatic potentials, in order
to compare different gerrymandering strategies. Due to the probabilistic
population fluctuations inherent to our voter models, Monte Carlo methods can
be applied to the districts constructed via our gerrymandering algorithms.
Through Monte Carlo studies we quantify the effectiveness of each of our
gerrymandering algorithms and we also argue that gerrymandering strategies
which do not include spatial data lead to (legally prohibited) highly
disconnected districts. Of the three algorithms we propose, two are based on
different strategies for packing opposition voters, and the third is a new
approach to algorithmic gerrymandering based on genetic algorithms, which
automatically guarantees that all districts are connected. Furthermore, we use
our lattice voter model to examine the effectiveness of isoperimetric quotient
tests and our results provide further quantitative support for implementing
compactness tests in real-world political redistricting.
