The following is a guest post from Sandy Gordon (NYU Politics), Doug Spencer (Colorado Law), and Sidak Yntiso (Rochester Poli Sci), discussing their newly published article — “What is the Harm in (Partisan) Gerrymandering? Collective vs. Dyadic Accounts of Representational Disparities” — in the (peer-reviewed) Journal of Legal Analysis.
As Texas, Missouri, and (likely) California plunge the country back into the latest round of redistricting wars, the overwhelming majority of coverage and commentary has focused on the collective consequences of re-gerrymandering: how will these maneuvers affect majority control of the House of Representatives come 2027, and how do they affect the relationship between the partisan makeup of the states in question and the partisan composition of their respective delegations to Congress?
In a deeply polarized country with highly nationalized politics, the focus on collective consequences is understandable. And yet lost in the discussion is the impact of these maneuvers on the “dyadic” relationship between individual voters and their representatives. A dyadic perspective considers questions such as whether legislators share the values of their own constituents, whether they are competent, and whether they work hard for their communities. Not only are these the criteria by which many citizens judge their democracy; dyadic conceptions of representation also resonate with the geographic organization of Congress and the Constitution’s emphasis on individual, rather than collective, rights and harms.
In our new article, “What is the Harm in (Partisan) Gerrymandering? Collective vs. Dyadic Accounts of Representational Disparities,” published in the Journal of Legal Analysis, we explore a general account that centers the dyadic relationship of voters and their representatives in debates about the fairness of districting plans.
When is a Map Fair to Voters?
To capture the intuition, consider an imaginary state composed of nine voters—five Republicans and four Democrats—evenly divided among three districts. Three maps are proposed: A, B, and C. In Map A, Republicans have a 2–1 majority in Districts 1 and 2 and Democrats have a 1–2 majority in District 3. In Map B, Republicans have a 3–0 majority in District 1 and a 2–1 majority in District 2, while Democrats enjoy a 0–3 majority in District 3. In Map C, Republicans have a 3–0 majority in District 1, and Democrats a 1–2 majority in Districts 2 and 3.
Focus for the moment on a comparison between Maps A and B. Which is more fair? If all that matters is how closely the partisan breakdown of the elected assembly matches that of the electorate, there’s no meaningful difference between the two partitions: Both may be expected to generate a delegation consisting of one Democratic and two Republican legislators. And with nine voters and three legislators, this is as close as you can get to proportionality—one possible criterion for collective fairness.
From a dyadic perspective, however, the maps are not the same—but why they differ depends on what voters ultimately care about. In Map A, six out of nine voters have a representative from their own party, while in Map B, eight out of nine do. So, if voters only care about having a representative who shares their values, Map B is a clear winner. But suppose voters are apprehensive of lopsided majorities—perhaps because these encourage shirking by incumbent legislators. In that case, Map A might be preferable.
Now look at Map C: no matter what collective or dyadic criterion you employ, this third map is unfair.
Our paper generalizes the intuition from these examples by presenting a stylized formal model that grounds the welfare of voters in terms of (a) the correspondence between their values and those of their legislator (as captured by co-partisanship); (b) legislator competence; and (c) legislator incentives to work hard on behalf of their constituents.
The model yields measures of “representational disparity” that capture how fairly different groups of voters (e.g., Republicans and Democrats) are treated under a given map. As with collective metrics such as the efficiency gap and partisan bias, the measure can be tested across ensembles of millions of alternative maps, revealing whether an enacted plan is a true outlier or simply reflects the geographic distribution of a state’s voters.
Critically, these measures can be “tuned” to reflect features of the underlying political environment and the user’s commitment to different, potentially contradictory values. For example, if matching legislator and constituent partisanship is the overriding concern, then a map that makes districts maximally non-competitive might come closest to achieving that objective. But if motivating legislators to work hard on behalf of a broad range of constituents matters, then the measure will reward more competitive plans.
What the Evidence Shows
Relationship to existing measures. While our approach forges new conceptual ground, our measures will generally be correlated, though imperfectly so, with existing measures like partisan bias, efficiency gap, and declination. But situations may arise where our dyadic commitments lead to different substantive conclusions than collective ones would.
Examples from the paper. Using examples from a handful of states, our article shows that traditional metrics often miss the mark. For instance, in Massachusetts, Republicans rarely win congressional seats—not necessarily because of gerrymandering, but because their voters are too evenly spread out. Dyadic analysis reveals more nuanced harms: while all maps disadvantage Republicans collectively, some alternatives give them better representation at the district level. By contrast, in Florida and Pennsylvania, enacted maps emerge as extreme outliers under both collective and dyadic metrics, making the case for unfairness much clearer.
Analyzing the 2025 Texas and California Maps. Using the approach described in our article, we conducted an outlier analysis to assess the extremity of the enacted Texas and proposed California maps on dyadic representational grounds under two different “tunings” of representational disparity. Here’s a comparison of the 2021 and 2025 Texas maps with an ALARM ensemble of simulated maps. (In all graphs, the solid vertical line indicates zero disparity.)
As the figures indicate, the 2021 Texas map was already an extreme outlier irrespective of how the measure is tuned. The new map is even more extreme.
Here’s our analysis of California:
Our analysis suggests that according to the first version of the measure, which prioritizes matching constituent and legislator partisanship, the 2021 California map is not an outlier, but the 2025 proposed map would be. According to the second version, which rewards competitiveness, both maps are extreme outliers, but the 2025 plan would be worse.
Why This Matters
It is certainly not clear (to us) that single-member districts are the most effective way to select our representatives. Yet it is the system we have, and a system of representation inescapably rooted in geographic districts must be evaluated using diagnostics that treat districts and their boundaries not merely as an inconvenience but as an intrinsic feature. Gerrymandering isn’t just about partisan balance sheets—it’s also about whether citizens can trust that their voices are heard in the halls of power.
