The Statistical Properties and Empirical Performance of Double Regression

Voting rights litigation requires ecological inference to estimatethe voting preferences of minority and nonminority groups withinthe electorate. Double regression has been the procedure mostcommonly employed for this purpose. This article presents thefirst formal examination of this procedure. The underlying structuralmodel reveals that double regression estimators are neitherunbiased nor consistent estimators of true within-group votepreferences or polarization. Simulations demonstrate that theycan substantially exaggerate the differences between minorityand nonminority vote choices when none are present, and dramaticallyunderstate them when differences exist. In sum, double regressioncannot meet conventional statistical standards for reliability.Consequently, it should be abandoned.