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Scholars and legal practitioners of voting rights are concerned with estimating individual-level voting behavior from aggregate-level data. The most commonly used technique, King's ecological inference (EI), has been questioned for inflexibility in multiethnic settings or with multiple candidates. One method for estimating vote support for multiple candidates in the same election is called ecological inference: row by columns (R×C). While some simulations suggest that R×C may produce more precise estimates than the iterative EI technique, there has not been a comprehensive side-by-side comparison of the two methods using real election data that analysts and legal practitioners often rely upon in courts. We fill this void by comparing iterative EI and R×C models with a new statistical package--eiCompare--in a variety of R×C combinations including 2 candidates and 2 groups, 3 candidates and 3 groups, and up to 12 candidates and three groups and multiple candidates and four groups. Additionally, we examine the two methods with 500 simulated data sets that differ in combinations of heterogeneity, polarization, and correlation. Finally, we introduce a new model congruence score to aid scholars and voting rights analysts in the substantive interpretation of the estimates. Across all of our analyses, we find that both methods produce substantively similar results. This suggests that iterative EI and R×C can be used interchangeably when assessing precinct-level voting patterns in Voting Rights Act cases and that neither method produces bias in favor or against finding racially polarized voting patterns.

Scholars and legal practitioners of voting rights are concerned with estimating individual-level voting behavior from aggregate-level data. The most commonly used technique, King's ecological inference (EI), has been questioned for inflexibility in multiethnic settings or with multiple candidates. One method for estimating vote support for multiple candidates in the same election is called ecological inference: row by columns (R×C). While some simulations suggest that R×C may produce more precise estimates than the iterative EI technique, there has not been a comprehensive side-by-side comparison of the two methods using real election data that analysts and legal practitioners often rely upon in courts. We fill this void by comparing iterative EI and R×C models with a new statistical package—eiCompare—in a variety of R×C combinations including 2 candidates and 2 groups, 3 candidates and 3 groups, and up to 12 candidates and three groups and multiple candidates and four groups. Additionally, we examine the two methods with 500 simulated data sets that differ in combinations of heterogeneity, polarization, and correlation. Finally, we introduce a new model congruence score to aid scholars and voting rights analysts in the substantive interpretation of the estimates. Across all of our analyses, we find that both methods produce substantively similar results. This suggests that iterative EI and R×C can be used interchangeably when assessing precinct-level voting patterns in Voting Rights Act cases and that neither method produces bias in favor or against finding racially polarized voting patterns. [ABSTRACT FROM AUTHOR]