Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2406.12167

Bounds and Bugs: The Limits of Symmetry Metrics to Detect Partisan Gerrymandering

Daryl DeFord·Ellen Veomett
View original source ↗Read source document ↗Export metadata ↓

Abstract

We consider two symmetry metrics commonly used to analyze partisan gerrymandering: the Mean-Median Difference (MM) and Partisan Bias (PB). Our main results compare, for combinations of seats and votes achievable in districted elections, the number of districts won by each party to the extent of potential deviation from the ideal metric values, taking into account the political geography of the state. These comparisons are motivated by examples where the MM and PB have been used in efforts to detect when a districting plan awards extreme number of districts won by some party. These examples include expert testimony, public-facing apps, recommendations by experts to redistricting commissions, and public policy proposals. To achieve this goal we perform both theoretical and empirical analyses of the MM and PB. In our theoretical analysis, we consider vote-share, seat-share pairs (V, S) for which one can construct election data having vote share V and seat share S, and turnout is equal in each district. We calculate the range of values that MM and PB can achieve on that constructed election data. In the process, we find the range of (V,S) pairs that achieve MM = 0, and see that the corresponding range for PB is the same set of (V,S) pairs. We show how the set of such (V,S) pairs allowing for MM = 0 (and PB = 0) changes when turnout in each district is allowed to vary. By observing the results of this theoretical analysis, we can show that the values taken on by these metrics do not necessarily attain more extreme values in plans with more extreme numbers of districts won. We also analyze specific example elections, showing how these metrics can return unintuitive results. We follow this with an empirical study, where we show that on 18 different U.S. maps these metrics can fail to detect extreme seats outcomes.

Explore related subjects

cs.CYmath.COphysics.soc-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Daryl DeFord, Ellen Veomett. 2025-07-11. Bounds and Bugs: The Limits of Symmetry Metrics to Detect Partisan Gerrymandering. https://doi.org/10.1089/elj.2024.0038

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A Brief AI Literacy Intervention Does Not Significantly Reduce Over-Reliance and Increases Under-Reliance on ChatGPT: A Randomized Study

In this study, we examined whether a brief AI literacy intervention influences high school students' reliance on recommendations from large language models (LLMs). In a randomized experiment, students were assigned to either a control group receiving a brief introduction to LLMs or an intervention group receiving additional information about how LLMs work, their limitations, and effective usage strategies. Participants then solved eight math puzzles with ChatGPT's advice, which was incorrect in half of the trials. Results indicated widespread over-reliance, with incorrect recommendations adopted in 52.1% of the trials. The intervention did not significantly reduce over-reliance. Instead, it led to an increase in under-reliance, as students were more likely to reject correct recommendations. These findings provide preliminary evidence that brief text-based interventions may be ineffective in fostering appropriate reliance. More comprehensive and interactive approaches may be required to meaningfully influence students' real-world reliance on LLMs.

cs.CY↗
arXiv2026

Examining Community-Requested Fact-Checking: Request Alerts Are Associated with Greater Diversity and Visibility of Community Notes

Crowdsourced fact-checking systems such as Community Notes are increasingly used on social media platforms, yet concerns remain about which content receives scrutiny and how visible that scrutiny is. X allows users to request notes for specific posts. When sufficient requests accumulate, an alert is displayed, creating an interface cue that may guide contributor behavior. We present a quantitative, non-causal analysis comparing the diversity and visibility of community notes written for X posts with and without request alerts. We infer alert presence at note submission and analyze 10,432 alerted and 44,442 non-alerted English notes from 318 top writers. We find that, alerted notes are associated with greater individual-level topical diversity, but also with stronger collective concentration in the Politics category. Mixed-effects models estimate that alerted notes are 8.4-20.2 percentage points more likely to be modeled helpful and visible, though this visibility gain diminishes as topics diverge from writers' prior interests.

cs.CY↗
arXiv2026

Scarcity and Predictive Uncertainty: Implications for Societal Resource Allocation

An emerging literature examines the critical question of when and how prediction can be useful in allocating scarce societal resources. We examine a novel variant of this question: What happens when predictive uncertainty differs systematically across the population? This can occur in several situations; for example, when machine learning models have significantly different accuracies across different demographics. We show that this uncertainty has serious implications for resource allocation when coupled with commonly used binary measures of societal benefit from allocation. We formulate a novel mathematical model of scarce resource allocation that accounts for heterogeneous predictive uncertainties and analyze implications for both the allocation mechanism and the realized population-level benefits. We find that when resources are very scarce, maximum marginal benefit (MMB) prioritization favors individuals with lower predictive uncertainty even at the identical underlying initial state. However, we observe a flip in prioritization when resources are abundant, targeting higher-uncertainty individuals. We illustrate the implications of our results on the PISA educational testing dataset. Our findings have meaningful ramifications for the distributional outcomes of prioritization policies in many domains touched by the theory of local justice, including the allocation of public education resources, medical triage, and homelessness services. They also reveal a new moral dilemma in the ethics of scarce resource allocation - is it just to allocate a resource to one person over another solely based on predictive uncertainty about their futures? We also assess efficiency losses under both MMB and the vulnerability-first (VF) prioritization. Our model predicts efficiency losses across all resource levels, but particularly in low-resource settings.

cs.CY↗