We consider the measures of partisan symmetry proposed for practical use in the political science literature, as clarified and developed in Katz, King, and Rosenblatt (2020, American Political Science Review 114, 164–178). Elementary mathematical manipulation shows the symmetry metrics to have surprising properties that call their meaningfulness into question. To accompany the general analysis, we study measures of partisan symmetry with respect to recent voting patterns in Utah, Texas, and North Carolina, flagging problems in each case. Taken together, these observations should raise major concerns about the available techniques for quantitative scores of partisan symmetry—including the mean–median score, the partisan bias score, and the more general “partisan symmetry standard”—with the decennial redistricting underway.

Katz, King, and Rosenblatt recently wrote a broad survey developing and extending the theory of partisan symmetry. Our paper reviewed the implementability of the theory, focusing on simplified scores of symmetry—seemingly compatible with their formulation—that are in wide use. We analyzed these simplified scores and concluded that they are not suited for redistricting reform. By our reading of their response, Katz, King, and Rosenblatt agree.