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. 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"-as the decennial redistricting begins.

American democracy is currently heavily reliant on plurality in single-member districts, or PSMD, as a system of election. But public perceptions of fairness are often keyed to partisan proportionality, or the degree of congruence between each party’s share of the vote and its share of representation. PSMD has not tended to secure proportional outcomes historically, partially due to gerrymandering, where line-drawers intentionally extract more advantage for their side. But it is now increasingly clear that even blind PSMD is frequently disproportional, and in unpredictable ways that depend on local political geography. In this paper we consider whether it is feasible to bring PSMD into alignment with a proportionality norm by targeting proportional outcomes in the design and selection of districts. We do this mainly through a close examination of the “Freedom to Vote Test,” a redistricting reform proposed in draft legislation in 2021. We find that applying the test with a proportionality target makes for sound policy: it performs well in legal battleground states and has a workable exception to handle edge cases where proportionality is out of reach.

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 symmetryseemingly 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.

We consider the measures of partisan symmetry proposed for practical use in the political science literature, as clarified and developed in [10]. Elementary mathematical manipulation shows the symmetry metrics derived from uniform partisan swing to have surprising properties. 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 using quantitative scores of partisan symmetry-including the mean-median score, the partisan bias score, and the more general "partisan symmetry standard"-as the decennial redistricting approaches.