To satisfy Gingles 2 and 3 (Module 9), you must prove that a minority class votes as a cohesive bloc and that the white majority votes universally against them. But in America, the ballot is secret. The state knows that a neighborhood is 60% Hispanic, and the state knows that Candidate A received 60% of the vote across that neighborhood. But you cannot simply assume every Hispanic voter voted for Candidate A—doing so is a statistical fallacy known as the "ecological fallacy." To legally prove Racially Polarized Voting (RPV) without violating the secret ballot, analysts deploy Ecological Inference (EI) to estimate individual behavior from aggregate data.
In This Module
- Covers: The ecological fallacy, homogeneous precinct analysis, and the statistical mechanics of Ecological Inference (EI).
- Why it matters: If you cannot successfully run an EI model, you cannot prove Racially Polarized Voting. If you cannot prove RPV, you cannot win a Section 2 lawsuit.
- After this module, the reader can: Understand the progression from "Homogeneous Precinct Analysis" to Bayesian Ecological Inference and know exactly which software packages to run.
Reading List
Conceptual
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We return to King's foundational text introduced in Course 2. Focus this time purely on the mathematics. King bounded the statistical possibilities (e.g., if a precinct is 80% Black and Candidate A won 90% of the vote, mathematically at least *some* Black voters had to vote for Candidate A). By cross-referencing these numerical boundaries across hundreds of precincts, the model computationally zeros in on true voting rates.
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A study of the methodological evolution. Before King's EI models, courts accepted "Homogeneous Precinct Analysis"—literally only looking at precincts that were 90%+ of a single race and assuming the entire demographic voted that way. Today, courts require advanced EI cross-checking against Ecological Regression (ER).
Methods
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An applied guide to taking EI into court. The authors show how to structure the analysis to ensure statistical significance. They highlight the scale problem: if you attempt to run EI on a local city council district where there are only 4 precincts, the algorithm will fail due to lack of geometric data points. The analyst must know the physical constraints of their models.
Technical Reference
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The literal software used to win cases. eiCompare is a standard open-source R package explicitly designed to seamlessly compare Ecological Inference estimates with Ecological Regression to prove RPV for court. Data scientists must familiarize themselves with this codebase to process their CVAP data efficiently.
Key Concepts
How does Gary King's Ecological Inference model estimate individual voting behavior from aggregate data?
King's EI model bounds statistical possibilities using deterministic constraints. If a precinct is 80% Black and Candidate A won 90%, mathematically at least some Black voters had to vote for Candidate A. By cross-referencing these boundaries across hundreds of precincts, the Bayesian framework produces posterior probability distributions with 95% confidence intervals for each group's estimated vote share—without violating ballot secrecy.
How did courts evolve from Homogeneous Precinct Analysis to Ecological Inference?
Courts initially accepted "Homogeneous Precinct Analysis"—examining only precincts 90%+ of a single race and assuming demographic uniformity. This was crude and limited. Modern courts require advanced Ecological Inference cross-checked against Ecological Regression to ensure robustness, moving from simple assumption to rigorous Bayesian estimation.
What scale constraints limit Ecological Inference in small jurisdictions?
Barreto and Collingwood highlight that EI fails in jurisdictions with very few precincts (e.g., a city council district with only 4). The algorithm requires a meaningful number of geographically diverse precincts with varying demographic compositions to triangulate voting behavior. Analysts must verify sufficient precinct-level variation before presenting EI results as evidence.
What is eiCompare and why is it the standard software for proving Racially Polarized Voting?
eiCompare is an open-source R package designed to compare Ecological Inference with Ecological Regression outputs. It processes CVAP data, generates side-by-side EI and ER comparisons, and produces publication-ready visualizations with confidence intervals. Courts increasingly expect standardized, reproducible software rather than custom scripts, making eiCompare the de facto standard.
Goal: Add the Ecological Inference protocol to your Methodology Portfolio.
Now that you have chosen the historical elections (Module 9), specify exactly how you will process them.
- State the Software: Declare the codebase you will use to run your analysis (e.g., "The analysis will deploy the eiCompare package in the R environment.")
- Establish the Threshold: Define what constitutes "Racially Polarized Voting" in your model. (e.g., "If the EI model shows the minority class coalescing behind a candidate at greater than 75%, and the white bloc voting against that candidate at greater than 60%, RPV is established.")
- Defend the Margin: Explicitly note that the EI outputs are estimates with 95% confidence intervals, not absolute certainties, protecting your methodology from hostile cross-examination.