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Abstract

We offer a simple use of Bayes' Theorem to model the relationship between surname and ethnicity in order to improve present expert witness practices in voting rights litigation. Our aim is to show how to better estimate the overall Hispanic share of the electorate to determine realistic opportunity to elect candidates of choice. We show that there is no such thing as the proportion of bearers of a given name who are Hispanic. How “Hispanic” any given name turns out to be is a function of the overall Hispanicity of the population, which affects both the distribution of names and the conditional probability that the possessor of any given name will be Hispanic. Because of this, the number of names on a surname list (say that of registered voters) that should be counted as Hispanic is not fixed, but rather varies by demographic context. We show how to identify the optimal size of a surname list by balancing false positives and false negatives. We also provide some “quick and dirty” approximation methods for estimating the size of an optimal surname list. For example, the optimal number of names needed for a national sample, which is 13.4 percent Hispanic, is roughly 4,300 names. Too many names and you overstate Hispanic population; too few and you understate it. This list of 4,310 surnames, rather counterintuitively, includes all surnames whose holders have more than 34 percent probability of self-identifying as of Spanish heritage on the Census. However, we also show that, despite the existence of both false positives and false negatives, ecological inference of racial bloc voting (RBV) patterns using surname-based estimates of the Hispanic share of the electorate at the voting tabulation unit level as the independent variable will usually give us results that are more robust to error in list size than calculations of overall Hispanic levels. In the former case, the two types of error will tend to occur in geographic locations in ways that limit their consequences for the accuracy of RBV estimates.

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Using Spanish Surname to Estimate Hispanic Voting Population in Voting Rights Litigation: A Model of Context Effects Using Bayes' Theorem

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