  Assuming that partisan fairness and responsiveness are important aspects of
redistricting, it is important to measure them. Many measures of partisan bias
are satisfactory for states that are balanced with roughly equal proportions of
voters for the two major parties. It has been less clear which metrics measure
fairness robustly when the proportion of the vote is unbalanced by as little as
60% to 40%. We have addressed this by analyzing past election results for four
states with Democratic preferences (CA, IL, MA, and MD), three states with
Republican preferences (SC, TN, and TX) and comparing those to results for four
nearly balanced states (CO, NC, OH, and PA). We used many past statewide
elections in each state to build statistically precise seats for votes and rank
for votes graphs to which many measures of partisan bias were applied. In
addition to providing values of responsiveness, we find that five of the
measures of bias provide mutually consistent values in all states, thereby
providing a core of usable measures for unbalanced states. Although all five
measures focus on different aspects of partisan bias, normalization of the
values across the eleven states provides a suitable way to compare them, and we
propose that their average provides a superior measure which we call composite
bias. Regarding other measures, we find that the most seemingly plausible
symmetry measure fails for unbalanced states. We also consider deviations from
the proportionality ideal, but using it is difficult because the political
geography of a state can entangle responsiveness with total partisan bias. We
do not attempt to separate intentional partisan bias from the implicit bias
that results from the interaction of the map drawing rules of a state and its
political geography, on the grounds that redistricting should attempt to
minimize total partisan bias whatever its provenance.
