'Partisan Bias' is Like 'Cancer'

Abstract: The colloquial phrase "partisan bias" encompasses multiple distinct conceptions of bias, including partisan advantage, packing & cracking, and partisan symmetry. All are useful and have their place, and there are several proposed measures of each. While different measures frequently signal the direction of bias consistently for redistricting plans, sometimes the signals are contradictory: for example, one metric says a map is biased towards Democrats while another metric say the same map is biased towards Republicans. This happens most frequently with metrics that measure different kinds of bias, but it also occurs between measures in the same category. These inconsistencies are most pronounced in states where one party is dominant, but they also occur across the full range of partisan balance. The political geography of states also influences the frequency with which various measures are inconsistent in their assessment of bias. No subset of metrics is always internally consistent in their signal of bias.