  Geographical considerations such as contiguity and compactness are necessary
elements of political districting in practice. Yet an analysis of the problem
without such constraints yields mathematical insights that can inform
real-world model construction. In particular, it clarifies the sharp contrast
between proportionality and competitiveness and how it might be overcome in a
properly formulated objective function. It also reveals serious weaknesses of
the much-discussed efficiency gap as a criterion for gerrymandering.
